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Unformatted text preview: ‘ Math 201 — Test 3 _
Section: Name‘M Show appropriate work to receive credit on all problems and place your answer in the blank provided. Point value of each problem is
listed in the problem statement. Calculators are not allowed on this exam. ' ’ C132 9 2 4
1. If matrix A = 1 5 ﬁnd a 32 and the size (ie order) of A: (2 points each) or}:
3 8 O\\OJ 2 1 3 2 —1 2
2, GivenA= [ ] , 13 = [ ] ﬁnd(A+B)T. (5 points) . 1 —I 0
3. Perform the indicated operation and simplify your answer: [2 0 4] S 3 4 ._ (5 points)
ierSwxez) [xv + our; ~r ox.’ . 4mg” «3
lXVH‘J’ﬁ §+ﬂ¥l~2) 29:0 Hf 0X3 + (Fit a; i 4. HA is a 3 X 5 matrix, B is a 5 X 7 matrix, C is a 7 >< 11 matrix, D is a 5 X 7 matrix, which ofthe following matrix
products are deﬁned? Give the size of each answer if it is deﬁned. (12 points) Deﬁned? (yes/no) Size (order) if deﬁned:
a.)A><B><C gas __%_A_l_l_’ ”
b.)A><D><C 365 351] c.) B X C X D “(143 5. Classify each of the following as True or False by circling the correct letter. (3 points each) 1030 a.) If a reduced matrix for a linear system is 0 1 2 0 , then the system has no solution. T @
0 0 0 0 1 o 3 0
b.) If areduced matrix foralinear system is 0 1 2 0 ,then the system has inﬁnitely many solutions. T @
0 0 o 1 6. Solve each system of equations by creating an augmented matrix for the system and reducing that matrix. State your
answer in terms of a parameter or parameters if needed. ( a: 6 points, 1): 8 points) a) x—y=5 7 I A gag
‘ [email protected]=—2 i“ I a‘ 8 ”
1\ 5 ~1Rt+§zi‘l(5]b\e2[ [ \ 1 O b «a; O 1 “‘2;
LL it "‘ "'
Rani?! I O ] 3 1
[o l *1
2x+3y—z:8
b.) x—y+22=~l «:1133‘232"
'—x+2y+z=—1
313% E? 9R; 1 “"i 9' ‘4 maﬁaHQ; i H 2 “I L
I e 2 ti h D 3— 3 "*i E’ ‘ ,‘> .t ...i‘ J 6:! , _ f1 E .3. :‘m _, or: :3 f2.— ,
H‘ll“! [all' ‘101+’100‘a
. “it“25 s. R5  .2. 0 I '3
oitlhRnﬁQOiia 0‘ »R5~rt2.00].4
0 1 3‘1‘ 50 06+“ 0 O i”  7 21.) Write the system of equations below as a matrix equation in the form AX: B: (2 points) w+wzz 6 §'% :Yll
x + y 2 *3 Matrix Equation:£ f I a] “5‘. b.) Find the inverse, that is A"‘, for the coefﬁcient matrix A from part 7a above. Use techniques shown in the text. , (6noints) — _ '
U f L ﬁrst; H“? n HD ;‘ “ﬁr {30 [Ev—92142,}? 0’; ~]
Mioaileb )0 i *1 15 0 iiel b C.) Use A’1 to solve the system given in 7a (4 points) Solution: : i mat. “513%; «new 8‘ Maximize Z = ﬁrs43; subject to constraints x + 2y 5 10, x 5 4, y 3 2, x20 , yZOusing the linear
programming techniques detailed below. Show all appropriate work. (18 points) Graph the feasible region. Indicate whether
you left the ﬁaasible region shaded or
(Circle one.) " 9. Problem Statement: Coordinates of vertices (corners) of feasible region: Cit,3) ! (c s)! (all), (4152) Process to maximize E
s. s o ‘3 ' I 0
0 l
a ‘2— 2c _ Value of Z and coordinates at the maximum: 3:22 a) (33) A manufacturer produces two products, product/1 and product B. Both products require processing on Machine I and H. The
number of hours needed to produce one unit is given in the chart below. Machine I is available for at most [000 hours per month
and Machine 11 is available for at most 2400 hours per month. The proﬁt made on product A is $10/unit and the proﬁt made on
product B is 15/unit. Find the production level that will maximize proﬁt and find the maximum proﬁt. Complete the table, identify variables and set up the objective function & the constraints only. Do not solve. (10 points)  Machine I Machine I] Insert Profit Values Product A ‘ 2 hr 3 hrs Product B i 1 hrs 4 hrs Unknowns (be precise): x: Jr'EWdZMA
y: a Pmin iloiuwC/‘t Constraints: W00
3 +¢t~ $2. 0 0 Objective Function: 1 [0 '1‘ ‘ \3’ 10. Use Simplex method to maximize Z = 2x; + x2 subject to 361 +2x2 £8
2251+3x2 S12 xl,x220 Complete each of the following steps: Write constraints stated as equations With slack variables here: (4 points) '><\+2><.~._ + 31 2—52
21X\’{ 3X1 +3?— "ill initial Table: 7 _ ' '
’Xl 7(1. 3‘ g; g \Q ‘ aatieaminaei I (12 points) ...
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 Spring '08
 SMITH
 Optimization

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