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Course: MATH 171A, Spring 2012
School: UCSD
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Linear Recap: programs in standard form Math 171A: Linear Programming Lecture 21 Linear Programs in Standard Form Philip E. Gill c 2011 minimize n xR c Tx Ax = b , x 0 simple bounds subject to equality constraints The matrix A is m n with shape A = We apply &quot;mixed-constraint&quot; simplex with full matrix A I http://ccom.ucsd.edu/~peg/math171a Friday, February 25th, 2011 UCSD Center for...

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Linear Recap: programs in standard form Math 171A: Linear Programming Lecture 21 Linear Programs in Standard Form Philip E. Gill c 2011 minimize n xR c Tx Ax = b , x 0 simple bounds subject to equality constraints The matrix A is m n with shape A = We apply "mixed-constraint" simplex with full matrix A I http://ccom.ucsd.edu/~peg/math171a Friday, February 25th, 2011 UCSD Center for Computational Mathematics Slide 2/44, Friday, February 25th, 2011 Example 2 3 2 1 1 1 0 constraint #1 constraint #2 constraint #3 constraint #4 constraint #5 constraint #6 constraint #7 1 1 = 0 -1 1 1 x1 ,x2 ,x3 ,x4 ,x5 minimize -6x1 - 9x2 - 5x3 2x1 + 3x2 + x3 + x4 =5 x1 + 2x2 + x3 - x5 = 3 x1 0 x2 0 x3 0 x4 0 x5 0 subject to A I 1 1 Consider the vertex defined by: the two rows of A rows 3, 4, and 5 of D = I , i.e., rows 5, 6 and 7 of A I UCSD Center for Computational Mathematics Slide 3/44, Friday, February 25th, 2011 UCSD Center for Computational Mathematics Slide 4/44, Friday, February 25th, 2011 A Dk 2 1 = 3 2 1 1 1 constraint #1 0 -1 constraint #2 constraint #5 constraint #6 1 constraint #7 1 1 0 2 1 3 2 1 1 1 1 0 x1 5 0 -1 x 2 x3 x4 1 1 x5 3 =0 0 0 These equations are block upper-triangular, with structure: B 0 N In-m 3 2 xB xN = b 0 This defines a vertex since rank A Dk =5=n with B= 2 1 and N = 1 1 1 0 0 -1 UCSD Center for Computational Mathematics Slide 5/44, Friday, February 25th, 2011 UCSD Center for Computational Mathematics Slide 6/44, Friday, February 25th, 2011 2 3 2 1 1 1 1 0 x1 5 1 1 x =0 0 0 1 0 -1 x 2 x3 x4 1 1 x5 and = 5 3 3 =0 0 0 x is a basic solution of Ax = b Then, x 3 = x 4 = x 5 = 0, 2 3 1 2 x1 x2 Every vertex is like this, i.e., it has n - m zero components and m nonnegative components. x1 x2 = 1 1 e.g., consider the vertex defined by rows 3, 5, and 7 of A . I UCSD Center for Computational Mathematics Slide 7/44, Friday, February 25th, 2011 UCSD Center for Computational Mathematics Slide 8/44, Friday, February 25th, 2011 From the previous slide: 2 3 2 1 1 1 1 0 constraint #1 0 -1 constraint #2 constraint #3 constraint #5 1 constraint #7 x1 5 2 3 2 1 1 1 1 0 x1 5 1 1 1 1 0 -1 x 2 x3 x4 1 x5 3 =0 0 0 2 3 2 1 1 1 1 0 Swap variables x 1 and x 4 . 1 0 3 2 1 1 1 2 0 x4 5 1 1 0 -1 x 2 x3 x4 1 x 5 3 =0 0 0 1 -1 x 2 x3 1 x1 1 x5 3 =0 0 0 UCSD Center for Computational Mathematics Slide 9/44, Friday, February 25th, 2011 UCSD Center for Computational Mathematics Slide 10/44, Friday, February 25th, 2011 From the previous slide: 1 3 2 1 1 1 2 0 x4 5 From the previous slide: 1 3 2 1 1 1 2 0 x4 5 0 1 -1 x 2 x3 1 x1 1 x5 3 =0 0 0 0 Swap equations 3 and 4. 1 3 2 1 1 1 2 0 x4 5 1 -1 x 2 x3 x1 1 1 x5 and 5 3 3 =0 0 0 In this case, x 1 = x 3 = x 5 = 0, 1 0 3 2 x4 x2 = 0 1 -1 x 2 x3 x1 1 1 x5 3 =0 0 0 x4 x2 = 1 2 3 2 UCSD Center for Computational Mathematics Slide 11/44, Friday, February 25th, 2011 UCSD Center for Computational Mathematics Slide 12/44, Friday, February 25th, 2011 From the previous slide: 1 3 2 1 1 1 x4 1 -1 x 2 x3 x1 1 1 x5 2 0 5 3 =0 0 0 Recap: Finding a basic solution of Ax = b 0 Define a column basis {1 , 2 , . . . , m } Gather the basis B of m linearly independent columns from A: B = a 1 Solve BxB = b for xB Rm . a2 am 0 Scatter xB into a zero x, i.e., xj = x is another basic solution of Ax = b [ xB ]i 0 if aj is the ith column of B; otherwise 3 2 x =0 1 2 0 UCSD Center for Computational Mathematics Slide 13/44, Friday, February 25th, 2011 UCSD Center for Computational Mathematics Slide 14/44, Friday, February 25th, 2011 x i = 0 at a vertex x means that the constraint xi 0 is active. Result A vertex of the feasible region: F = {x : Ax = b, x 0} is a nonnegative basic solution of Ax = b. In other words, if B is the basis associated with the vertex, then BxB = b with xB 0. Result A nondegenerate vertex of the feasible region: F = {x : Ax = b, x 0} is a nonnegative basic solution of Ax = b with precisely n - m zero components. i.e., if B is the basis associated with a nondegenerate vertex, then BxB = b with xB > 0. UCSD Center for Computational Mathematics Slide 15/44, Friday, February 25th, 2011 UCSD Center for Computational Mathematics Slide 16/44, Friday, February 25th, 2011 Result A degenerate vertex of the feasible region: F = {x : Ax = b, x 0} is a nonnegative basic solution of Ax = b with more than n - m zero components. i.e., if B is the basis associated with a degenerate vertex, then BxB = b with [ xB ]i = 0 for some i. Our aim is to restate the simplex method so that equations of size m m are solved The restated method computes the same sequence of vertices as the simplex method. UCSD Center for Computational Mathematics Slide 17/44, Friday, February 25th, 2011 UCSD Center for Computational Mathematics Slide 18/44, Friday, February 25th, 2011 We assume that A has rank m, i.e., A has independent rows. A mn At a vertex we can partition the variables (i.e., columns) into two sets B and N , where: 1 B is the basic set: B = {1 , 2 , . . . , m } column indices of A The basis is B = a1 2 a 2 am N is the nonbasic set N = {1 , 2 , . . . , n-m } B mm nonsingular UCSD Center for Computational Mathematics Slide 19/44, Friday, February 25th, 2011 column indices of A not in B N = a1 a2 an-m is the matrix of columns not in B. UCSD Center for Computational Mathematics Slide 20/44, Friday, February 25th, 2011 A variable is either basic (i.e., "free") or nonbasic (at its bound). Variables xi with i B are called basic variables. Variables xi with i N are called nonbasic variables. At a nondegenerate vertex, the terms "basic" and "active" are opposites. xi being basic constraint xi 0 is inactive. active. The working set for the mixed-constraint simplex method has the form: Ak = A Ik b 0 rows of In and bk = components from 0n xi being nonbasic xi constraint 0 is UCSD Center for Computational Mathematics Slide 21/44, Friday, February 25th, 2011 UCSD Center for Computational Mathematics Slide 22/44, Friday, February 25th, 2011 For example: 2 1 = 1 3 2 1 1 1 0 0 -1 1 2 3 2 1 1 1 1 0 1 1 column # of A #2 A Ik 0 -1 1 #3 #4 1 #5 #1 Basic set B = {2, 5}, nonbasic set N = {1, 3, 4}. Define the column permutation matrix P such that Ak P = B 0 N In-m P= 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 UCSD Center for Computational Mathematics Slide 23/44, Friday, February 25th, 2011 UCSD Center for Computational Mathematics Slide 24/44, Friday, February 25th, 2011 2 3 2 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 3 0 2 1 1 1 1 1 1 Matlab commands to find the permuted matrix AP. First method (preferred): Perm = [ 2 5 1 3 4 ] Aperm = A(:,Perm); % column list in order B-N % compute the permuted A 1 1 0 -1 1 0 0 1 0 0 2 -1 0 = 1 0 0 1 This gives B= 3 0 2 -1 and N = 2 1 1 1 1 0 Second method: I = eye(5,5); P = I(:,Perm); Aperm = A*P; % define the identity matrix % Define the column permutation matrix: % compute the permuted A UCSD Center for Computational Mathematics Slide 25/44, Friday, February 25th, 2011 The column permutation matrix P is such that A Ik P = Ak P = B 0 N In-m The column permutation applied to a row vector produces a row vector with basic part first. T c TP = cB T cN P Tc = cB cN xB xN pB pN The permutation moves the basic variables to the front. T x TP = xB T xN P Tx = Result The matrix Ak is nonsingular if and only if B is nonsingular. Proof: Homework. T p TP = pB T pN P Tp = UCSD Center for Computational Mathematics Slide 27/44, Friday, February 25th, 2011 UCSD Center for Computational Mathematics Slide 28/44, Friday, February 25th, 2011 The same goes for matrices: AP = B N and I k P = 0 In-m so that A Ik P= B N 0 IN = Result P is an orthogonal matrix, i.e., P TP = I = PP T . T Applying the column permutation P T to cB T cN returns c T : 0 IN Also T cB T cN = c TP T cB T cN P T = c TPP T = c T P cB cN = PP T c = c UCSD Center for Computational Mathematics Slide 29/44, Friday, February 25th, 2011 UCSD Center for Computational Mathematics Slide 30/44, Friday, February 25th, 2011 The simplex multipliers satisfy ATk = c. k The vertex xk defined by the simplex working set satisfies Ak xk = bk Ak PP T xk (Ak P)(P T xk ) B N 0 IN xB xN = bk = bk = b 0 BT NT Multiplying by P T gives P TATk = P Tc k (Ak P)Tk = P Tc 0 k = IN cB cN If the multipliers are partitioned as k = then zN BT NT multipliers for Ax = b multipliers for x 0 0 IN zN cB cN BxB + NxN = b xN = 0 BxB = b Note: to avoid clutter, we don't put a suffix on B or N. = UCSD Center for Computational Mathematics Slide 31/44, Friday, February 25th, 2011 UCSD Center for Computational Mathematics Slide 32/44, Friday, February 25th, 2011 Observe that BT NT 0 IN zN cB cN P Tz = zB zN = P T(c - AT) = P Tc - P TAT = P Tc - (AP)T c BT = B - cN NT = but B T = cB cB - B T = 0. the reduced costs associated with the basic variables are zero. cB - B T cN - N T = B T = cB zN = cN - N T Recall that z = c - AT are the reduced costs. zN are the reduced costs for the nonbasic variables. UCSD Center for Computational Mathematics Slide 33/44, Friday, February 25th, 2011 UCSD Center for Computational Mathematics Slide 34/44, Friday, February 25th, 2011 kth iteration STEP 1: Check for optimality Solve the equations AT k = c. k Solve B T = cB . Simplex Method for Standard Form Compute zN = cN - N T. If [ zN ]i 0 for i = 1, 2, . . . , n - m, then STOP. Otherwise, define [ zN ]s = min(zN ). The s-th nonbasic variable will become a basic variable. N = {1 , 2 , . . . , s , . . . , n-m } sth element of N UCSD Center for Computational Mathematics Slide 36/44, Friday, February 25th, 2011 kth iteration kth iteration STEP 2: (continued) Compute the search direction STEP 2: Compute the search direction Solve the equations Ak pk = em+s . B N 0 IN pB pN 0 es Solve BpB + NpN = 0 pN = es = BpB = -NpN = -Nes = -(sth column of N) = -(column s of A) we solve BpB = -as Increase xs while keeping other nonbasics fixed at 0 UCSD Center for Computational Mathematics Slide 37/44, Friday, February 25th, 2011 UCSD Center for Computational Mathematics Slide 38/44, Friday, February 25th, 2011 kth iteration kth iteration STEP 3: (continued) Step to an adjacent vertex What happens to the nonbasic variables? STEP 3: Step to an adjacent vertex If we take a step along the vector pB pN = pB es Then the new basic variables are: xB + pB all the basic variables change 0 0 . . . . . . 0 0 xN + pN = xN + es = xN + = row s 0 0 . . . . . . 0 0 all nonbasics remain at 0 except xs , which wants to increase. UCSD Center for Computational Mathematics Slide 39/44, Friday, February 25th, 2011 UCSD Center for Computational Mathematics Slide 40/44, Friday, February 25th, 2011 kth iteration STEP 3: (continued) Step to an adjacent vertex The changed variables are xB and xs (which increases from 0 to ) We must ensure that xB + pB 0 [ xB ]i -[ pB ]i i = + This is known as the min ratio test. Define = min{i } If = +, the LP is unbounded, STOP. if [ pB ]i < 0 if [ pB ]i 0 kth iteration STEP 3: (continued) Step to an adjacent vertex If = t then [ xB ]t + t [ pB ]t = 0 the t-th basic becomes nonbasic t points to index t of B s points to index s of N [ xB ]t 0 xt goes from basic to nonbasic [ xN ]s xs goes from nonbasic to basic UCSD Center for Computational Mathematics Slide 41/44, Friday, February 25th, 2011 UCSD Center for Computational Mathematics Slide 42/44, Friday, February 25th, 2011 kth iteration STEP 3: (continued) Step to an adjacent vertex Summary B {1 , 2 , . . . , s-1 , s , s+1 , . . . , m } moved from nonbasic set Two m m systems are solved: B T = cB BpB = -as Only the quantities , zN , xB pB need be computed N {1 , 2 , . . . , t-1 , t , t+1 , . . . , n-m } moved from basic set B and N exchange indices swap [ xB ]t = 0 and [ xN ]s = [ xB ]t = since xN is not stored (or re-solve BxB = b) column t of B is replaced by column s of A UCSD Center for Computational Mathematics Slide 43/44, Friday, February 25th, 2011 UCSD Center for Computational Mathematics Slide 44/44, Friday, February 25th, 2011
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UCSD - MATH - 171A
Recap: Simplex method for LPs in standard formMath 171A: Linear ProgrammingLecture 22 The Simplex Method for Standard FormPhilip E. Gillc 2011minimize nxRc Tx Ax = b , x 0simple boundssubject toequality constraintsWe apply &quot;mixed-constraint&quot; si
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UCSD - MATH - 171A
Math 171A: Linear ProgrammingConsider an LP in standard form: minimize nxRc Tx x 0Lecture 26 Interior Methods for Linear ProgrammingPhilip E. Gillc 2011subject to Ax = b, where A has m rows. The optimality conditions are: AT + z = c, Ax = b, x z =
UCSD - MATH - 171A
Math 171A Homework 1 SolutionsInstructor: Jiawang Nie January 24, 20121. Find the optimal solution to the following LP maximize x1 + 4x2 + 3x3 subject to 2x1 + x2 + x3 4 x1 - x3 = 1 x2 0, x3 0. Solution: The second equality constraint x1 = x3 + 1 allows
UCSD - MATH - 171A
Math 171A Homework 2 SolutionsInstructor: Jiawang Nie February 1, 20121. (8 points) Consider the feasible set F defined by the following constraints x1 + x2 4, x1 + 3x2 6, 6x1 - x2 18, 3 x2 6, x1 -1.(a) Express F in the standard form Ax b. Write down A
UCSD - MATH - 171A
Math 171A Homework 3 SolutionsInstructor: Jiawang Nie February 1, 20121. (4 points) For a given nonzero matrix A and nonzero vector b, assume that b may be written as b = bR + bN , where bR Range(A) and bN Null(AT ). (a) Show that bR and bN are unique.
UCSD - MATH - 171A
Math 171A Homework 4 SolutionsInstructor: Jiawang Nie February 14, 20121. (4 points) Consider the matrix of active constraints of an LP at a certain point x -1 -8 4 -7 -3 -4 2 0 4 -2 . Aa () = x -6 0 -3 3 5 0 0 5 2 7 Use Matlab to find a direction p alo
UCSD - MATH - 171A
Math 171A Homework 5 SolutionsInstructor: Jiawang Nie February 21, 20121. (5 points) Consider the linear program Minimize 3x1 subject to -2x1 x1 -2x1 2x1 x1 x2 -x2 +2x3 +4x2 +4x3 +4x2 +x3 +x2 +2x3 -2x2 -3x2 +x3 6 5 1 0 -2 0 0 x3 0and the point x = (1,
UCSD - MATH - 171A
Math 171A Homework 6 SolutionsInstructor: Jiawang Nie March 4, 20121. (5 points) Consider the LP of minimizing cT x subject to Ax b where 1 0 1 A= 1 0 0 1 1 0 0 1 0 0 1 1 , 0 0 1 2 5 4 b = , c = AT 1 1 1 0 1 1 . 1 0 0Find the minimizer of this LP by us
UCSD - MATH - 171A
Math 171A Practice Midterm IIInstructor: Jiawang Nie March 5, 20121. Consider the LP of minimizing c 2 3 A = 4 2 3x subject to Ax b where -15 3 5 -13 4 3 , b = -20 , c = A 5 1 -12 4 4 -13 5 2 0 1 0 . 1 1Find the minimizer of this LP by using optimali
UCSD - MATH - 171A
Math 171A Homework 1 SolutionsInstructor: Jiawang Nie January 24, 20121. Find the optimal solution to the following LP maximize x1 + 4x2 + 3x3 subject to 2x1 + x2 + x3 4 x1 - x3 = 1 x2 0, x3 0. Solution: The second equality constraint x1 = x3 + 1 allows
UCSD - MATH - 171A
Math 171A: Linear ProgrammingInstructor: Philip E. GillWinter Quarter 2011Homework Assignment #1 Due Friday January 14, 2011 I know that you are all aware of the importance of doing the homework assignments. This is the best way to keep up with the cla
UCSD - MATH - 171A
Math 171A: Linear ProgrammingInstructor: Philip E. GillWinter Quarter 2011Homework Assignment #1 Due Friday January 14, 2011 I know that you are all aware of the importance of doing the homework assignments. This is the best way to keep up with the cla
UCSD - MATH - 171A
Math 171A: Linear ProgrammingInstructor: Philip E. GillWinter Quarter 2011Homework Assignment #3 Due Friday January 28, 2011 Remember that the first midterm exam will be held in class on Wednesday, January 26. Starred exercises require the use of Matla
UCSD - MATH - 171A
Math 171A: Linear ProgrammingInstructor: Philip E. GillWinter Quarter 2011Homework Assignment #4 Due Friday February 4, 2011 Starred exercises require the use of Matlab. Exercise 4.1. Suppose that the constant vector c is such that cTp 0 for all p such
UCSD - MATH - 171A
Math 171A: Linear ProgrammingInstructor: Philip E. GillWinter Quarter 2011Homework Assignment #5 Due Friday February 11, 2011 Starred exercises require the use of Matlab. Exercise 5.1. Consider the set of inequality constraints Ax b, where 1 1 4 0 3 1
UCSD - MATH - 171A
Math 171A: Linear ProgrammingInstructor: Philip E. GillWinter Quarter 2011Homework Assignment #6 Due Friday February 18, 2011 Starred exercises require the use of Matlab. Exercise 6.1. (a) Consider the matrix of active constraints -1 -8 4 -7 -3 -4 2 0
UCSD - MATH - 171A
Math 171A: Linear ProgrammingInstructor: Philip E. GillWinter Quarter 2011Homework Assignment #7 Due Friday February 25, 2011 Starred exercises require the use of Matlab. Exercise 7.1. Consider the linear program of minimizing cTx subject to the genera
UCSD - MATH - 171A
Math 171A: Linear ProgrammingInstructor: Philip E. GillWinter Quarter 2011Homework Assignment #8 Due Friday March 4, 2011 The second midterm exam will be held in class on Wednesday, March 2. Starred exercises require the use of Matlab. Exercise 8.1. Co
UCSD - MATH - 171A
Math 171A: Linear ProgrammingInstructor: Philip E. GillWinter Quarter 2011Homework Assignment #9 Due Friday March 11, 2011 The final will be held Friday, March 18, 11:30am-2:30pm. Starred exercises require the use of Matlab. Exercise 9.1. Let a denote
UCSD - MATH - 171A
Math 171A: Mathematical ProgrammingInstructor: Philip E. GillWinter Quarter 2011Homework Assignment #1 Due Friday January 14, 2011 I know that you are all aware of the importance of doing the homework assignments. This is the best way to keep up with t
UCSD - MATH - 171A
Math 171A: Linear ProgrammingInstructor: Philip E. GillWinter Quarter 2011Homework Assignment #2 Due Friday January 21, 2011 The starred exercises require the use of Matlab. Remember that it is necessary to do all the Matlab assignments to obtain credi
UCSD - MATH - 171A
Math 171A: Linear ProgrammingInstructor: Philip E. GillWinter Quarter 2011Homework Assignment #3 Due Friday January 28, 2011 Remember that the first midterm exam will be held in class on Wednesday, January 26. Starred exercises require the use of Matla
UCSD - MATH - 171A
Math 171A: Linear ProgrammingInstructor: Philip E. GillWinter Quarter 2011Homework Assignment #4 Due Friday February 4, 2011 Starred exercises require the use of Matlab. Exercise 4.1. Suppose that the constant vector c is such that cTp 0 for all p such
UCSD - MATH - 171A
Math 171A: Linear ProgrammingInstructor: Philip E. GillWinter Quarter 2011Homework Assignment #5 Due Friday February 11, 2011 Starred exercises require the use of Matlab. Exercise 5.1. Consider the set of inequality constraints Ax b, where 1 1 4 0 3 1
UCSD - MATH - 171A
Math 171A: Linear ProgrammingInstructor: Philip E. GillWinter Quarter 2011Homework Assignment #6 Due Friday February 18, 2011 Starred exercises require the use of Matlab. Exercise 6.1. (a) Consider the matrix of active constraints -1 -8 4 -4 2 0 Aa = -
UCSD - MATH - 171A
Math 171A: Linear ProgrammingInstructor: Philip E. GillWinter Quarter 2011Homework Assignment #7 Due Friday February 25, 2011 Starred exercises require the use of Matlab. Exercise 7.1. Consider the linear program of minimizing cTx subject to the genera
UCSD - MATH - 171A
Math 171A: Linear ProgrammingInstructor: Philip E. GillWinter Quarter 2011Homework Assignment #8 Due Friday March 4, 2011 The second midterm exam will be held in class on Wednesday, March 2. Starred exercises require the use of Matlab. Exercise 8.1. Co
UCSD - MATH - 171A
Math 171A: Linear ProgrammingInstructor: Philip E. GillWinter Quarter 2011Homework Assignment #9 Due Friday March 11, 2011 The final will be held Friday, March 18, 11:30am-2:30pm. Starred exercises require the use of Matlab. Exercise 9.1. Let a denote
Cal Poly - MCB - 32
1. The Cori cycle involves formation of glucose made by gluconeogenesis in the liver from lactic acid produced by fermentation in skeletal muscles. True False 2. Skeletal muscle contains glucose 6-phosphatase to produce free glucose from glucose 6phosphat
Cal Poly - MCB - 32
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Cal Poly - MCB - 32
Number and Name I Olfactory II Optic III Oculomotor IV Trochlear V Trigeminal Mandibular Division VI Abducens VII Facial VIII Vestibulocochlear IX Glossopharyngeal X Vagus XI Accessory XII Hypoglossal Endocrine Gland Adipose Tissue Adrenal Cortex Adrenal
Cal Poly - MCB - 32
Number and Name I Olfactory II Optic III Oculomotor IV Trochlear V Trigeminal Mandibular Division VI Abducens VII Facial VIII Vestibulocochlear IX Glossopharyngeal X Vagus XI Accessory XII Hypoglossal Endocrine Gland Adipose Tissue Adrenal Cortex Adrenal
Cal Poly - MCB - 32
Guided Reading The Study of Body Function I 1. Blood plasma and interstitial fluid are separated from each other and there is little communication and exchange between these fluids. True False 2. The secretion of many hormones is regulated through negativ
Cal Poly - MCB - 32
Guided Reading - Enzymes and Energy I 1. Regulation of a metabolic pathway by the final product of the pathway is termed A. allosteric inhibition. B. end-product inhibition. C. negative feedback. D. Both end-product inhibition and negative feedback are co
Cal Poly - MCB - 32
Guided Reading - Cells and the Extracellular Environment I 1. Which of the following is a function of the steep Na+/K+ gradient across the cell membrane? A. provides energy for coupled transport B. creates electrochemical impulses C. maintains osmotic pre
Cal Poly - MCB - 32
Guided Reading - Cell Respiration and Metabolism I1. _ is the opposite of glycogenesis. A. Glycolysis B. Glyconeogenesis C. Glycogenolysis D. Gluconeogenesis 2. The process of fat formation from acetyl CoA is called A. lipogenesis. B. lipolysis. C. beta-
Cal Poly - MCB - 32
Guided Reading - Cell Respiration and Metabolism II1. Which of the following is a superoxide radical? A. an oxygen molecule with an extra, unpaired electron B. an oxygen molecule with two paired electrons C. hydrogen peroxide D. All of these choices are
Cal Poly - MCB - 32
Guided Reading - Cell Respiration and Metabolism II1. Which of the following is a superoxide radical? A. an oxygen molecule with an extra, unpaired electron B. an oxygen molecule with two paired electrons C. hydrogen peroxide D. All of these choices are
Cal Poly - MCB - 32
Guided Reading - Cell Respiration and Metabolism III1. Glycolysis converts glucose into two _ molecules. A. glycogen B. lactic acid C. acetyl CoA D. pyruvic acid2. Beta-oxidation of an 18 carbon fatty acid will yield _ acetyl CoA molecules. A. 9 B. 6 C.
Cal Poly - MCB - 32
Guided Reading - Cell Respiration and Metabolism III1. Glycolysis converts glucose into two _ molecules. A. glycogen B. lactic acid C. acetyl CoA D. pyruvic acid2. Beta-oxidation of an 18 carbon fatty acid will yield _ acetyl CoA molecules. A. 9 B. 6 C.
Cal Poly - MCB - 32
Guided Reading - Cell Structure and Genetic Control I1. Cells actively involved in secreting proteins would contain large numbers or quantities of A. lysosomes. B. peroxisomes. C. rough endoplasmic reticulum. D. smooth endoplasmic reticulum.2. Release o
Cal Poly - MCB - 32
Guided Reading - Cell Structure and Genetic Control I1. Cells actively involved in secreting proteins would contain large numbers or quantities of A. lysosomes. B. peroxisomes. C. rough endoplasmic reticulum. D. smooth endoplasmic reticulum.2. Release o
Cal Poly - MCB - 32
Guided Reading - Cell Structure and Genetic Control II1. Which of the following is NOT a molecular motor used to move substances along the cytoskeleton? A. melanin B. kinesin C. myosin D. dynein2. Which of the following locations have ciliated cells? A.
Cal Poly - MCB - 32
Guided Reading - Cell Structure and Genetic Control II1. Which of the following is NOT a molecular motor used to move substances along the cytoskeleton? A. melanin B. kinesin C. myosin D. dynein2. Which of the following locations have ciliated cells? A.
Cal Poly - MCB - 32
Guided Reading - Cell Structure and Genetic Control III1. The movement of chromosomes during mitosis is due to A. spindle fibers. B. telomeres. C. chromatids. D. actin and myosin.2. Small RNA and protein regions are joined together to make functional mR
Cal Poly - MCB - 32
Guided Reading - Cell Structure and Genetic Control IV1. The main function of the peroxisome is to release energy from food molecules and transform the energy into usable ATP. True False 2. Microtubules and microfilaments are the primary components of th
Cal Poly - MCB - 32
Guided Reading - Cells and the Extracellular Environment I1. Which of the following is a function of the steep Na+/K+ gradient across the cell membrane? A. provides energy for coupled transport B. creates electrochemical impulses C. maintains osmotic pre
Cal Poly - MCB - 32
Guided Reading - Cells and the Extracellular Environment II 1. Edema will result if a person has an abnormally low concentration of plasma proteins. True False 2. Osmoreceptors are involved in the regulation of blood volume. True False 3. Ion channels tha
Cal Poly - MCB - 32
Guided Reading Cells and the Extracellular Environment III1. The resting membrane potential is closest to the equilibrium potential for A. sodium ions. B. chloride ions. C. calcium ions. D. potassium ions.2. The transport maximum is related to the prope
Cal Poly - MCB - 32
Guided Reading - Cells and the Extracellular Environment IV 1. Which of the following is NOT a primary active transport pump? A. GLUT4 B. calcium pump C. sodium/potassium pump D. proton pump 2. What cofactor do matrix metalloproteinases need to be functio
Cal Poly - MCB - 32
Guided Reading - Chemical Composition of the Body I1. Molecules with polar covalent bonds are hydrophobic. True False2. How many single bonds can a carbon atom form if it is double-bonded to an oxygen atom? A. 1 B. 2 C. 3 D. 43. The ionized form of the
Cal Poly - MCB - 32
Guided Reading - Chemical Composition of the Body II1. Steroids are derived from cholesterol. True False 2. A blood pH of 7.6 is A. indicative of acidosis. B. indicative of alkalosis. C. in the normal physiological range. D. indicates effective buffering
Cal Poly - MCB - 32
Guided Reading - Chemical Composition of the Body III1. Lipids containing glycerol would include _ and _. A. triglycerides, steroids B. prostaglandins, phospholipids C. triglycerides, phospholipids D. steroids, prostaglandins2. The base that is NOT foun
Cal Poly - MCB - 32
Guided Reading - Enzymes and Energy I1. Regulation of a metabolic pathway by the final product of the pathway is termed A. allosteric inhibition. B. end-product inhibition. C. negative feedback. D. Both end-product inhibition and negative feedback are co
Cal Poly - MCB - 32
Guided Reading - Enzymes and Energy II1. Isomers are different forms of an enzyme. True False 2. During oxidation, a molecule or atom A. gains protons. B. loses protons. C. gains electrons. D. loses electrons. 3. Oxidized nicotinamide adenine dinucleotid
Cal Poly - MCB - 32
Guided Reading - Enzymes and Energy III1. Catalysts increase reaction rates by lowering the activation energy of a reaction. True False2. An enzyme elevated in the plasma of men with prostate cancer is A. alkaline phosphatase. B. catalase. C. creatine k