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Unformatted text preview: We Math 201 — Test 3 F 2
So lWJCTO Vt Show appropriate Work to receive credit on all problems and place your answer in the blank provided. Point value of each problem 1's
listed in the problem Statement. Calculators are not allowed on this exam. Section: Name: 2
1. If matrix A = 1
3 O\\D:l 4
5 ﬁnd a 23 and the size (ie order) of A: (2 points each)
8 1 2 3 2 —12
2. GivenA= [ l , B = [ ] ﬁnd(A+B)T. (5 points) 345 13—2
3&4 .9 r “T:
LAiﬁlr'" E 3
l
13‘ 1 —1 0
3. Perform the indicated operation and simplify your answer: [2 3 4] —2 3 .
I (Spomts)
ix1+L~4)xS~+ox(2) '15“? ‘1‘ll)xl+ 0X3 i~cr "‘l
lxilSxSF (ﬁll—Z) 1X0 "l" le “qugl 154' 4. If A is a 3 X 5 matrix, B is a 5 X 7 matrix, C is a 7 X 11 matrix, D is a 5 X 7 matrix, which of the following matrix
products are deﬁned? Give the size of each answer if it is deﬁned. (12 points) Deﬁned? ems/no) Size (order) if deﬁned:
,_‘.a.)A><B><C “6.3 EX H i
b.) B x C >< D no
c.)A><D><C $€S I 3X]! 5. Classify each of the following as True or False by circling the correct letter. (3 points each) 1 0 3 o
a.) If a reduced matrix foralinear system is 0 1 2 0 ,then the system has no solution. Cl“) F
0 0 0 1 1030 b.) If areduced matrix foralinear system is o 1 2 0 ,thenthe system has inﬁnitely many solutions. T
0 0 0 o  F 6. Solve each system of equations by creating an augmented matrix for the system and reducing that matrix. State your
answerin terms of a parameter or parameters if needed. ( a: 6 points, I): 8 points) adhyﬁ _:>_<;:_~t_'._
2x+'3y=‘—4 ‘ q t
i '1’ 1*12‘14321] ‘1‘ #3ng i i 3 ] 31,2
[3‘ C) 5‘ ——]o O l ‘2’
ﬂl‘tﬂb l O I i 1
O l "2
2x+3y—z=8 ‘
b.) {kw 222—1 "><:1 2 3:4
~x+2y+z:_1 _ ’1 =3 "*1 8 page“ 1 ~t 1 rt 2 + I *t 9 “‘i
*r K
\ ~\ l\‘ix § .1. 3 «1 g i; O J; ~S lo
Mfi .1 l "i
' i l .79? i ~ pm we we 0 __ 33,9
013—2 RldjooqJk 00 lago?
\
7 a.) Write the system of equations below asamatrix equation in the form AX = B: (2 points) ' 0 l ,4] 6x+5y=2 n . ~ 1
x + y z “3 Matrix Equation: 6 5 ’X 3: b.) Find the inverse, that is .44, for the coefﬁcient matrix A from part 7a above. Use techniques shown in the text, (6 points)
.55
t: 2).] 144: [ll (7 b 0 Eéﬁk’z l i
i] m t.” mum .1;]“**’">ié HI: Li‘WiLTH hf] c.) Use A'1 to solve the system giVen in 7a. (4 points) Solution: 7 L: i 2} [>532 [1‘ 11:] *— [Q] W” 8. Maximize Z = 4x + 2y subject to constraints x + 2y 5 10, x 5 4, y 3 1 x30 , y30using the linear
programming techniques detailed below. Show all appropriate work. (18 points) Graph the feasible region. Indicate whether you left thefeasibie region shaded or@
(Circle one.) Coordinates of vertices (corners) offensible region:
(14.3) to! s) ,(o .3). Gr 0 Process to maximize Z . i
you (ﬁr—,5); 2: 4(4) +243) :@
C633): 3: (mow—LS) :10 L0”): 5.:CFL o) +2 (1):; C MW; 2:4(LeHDLD312 Value of Z and coordinates at the maximum: 22. Mﬂ'gt 32 9. Problem Statement: A manufacturer produces two products, product A and product B. Both products require processing on Machine 1 and II. The
number of hours needed to produce one unit is given in the chart below. Machine I is available for at most 1000 hours per month
and Machine [I is available for at most 2400 hours per month. The proﬁt made on product/1 is $20/unit and the proﬁt made on
product B is $25/unii. Find the production level that will maximize profit ondfind the maximum proﬁt. Complete the table, identify variables and set up the objective function & the constraints only. Do not solve.
(10 points) Machine 1 Machine n Insert Proﬁt Values Product A _ 1 hr 3 hrs
Product B 2 hrs 4 hrs Unknowns (be precise): _ Constraints: 1% 2* ﬂ 3 l 09 O x: a: oiBroJini'A 31+ $13 if 00
y: g: “ilj‘twiwci‘i‘ 8 f5 2 % >¢ 0 Objective Function:_P_~_":—_2?l‘:l5‘ ‘3’ 10. Use Simplex method to maximize Z = 2x1 + x2 subject to x1 +le2 S8
234:I +3):2 _<_12 xv):2 20 Complete each of the following steps: Write constraints stated as equations with slack variables here: (4 points) ‘X1+9~XL+ S} 2?
1X\+3XL'+SI 1‘2“ 1nitidiSihz'pleLw'c'Tdble: " Vim andcohiinuef (12" points) I I Result: . 13 ‘ l
(11‘ 'Xl: f; M 062,2;0 ...
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This note was uploaded on 03/26/2012 for the course MATH 201 taught by Professor Smith during the Spring '08 term at Washington State University .
 Spring '08
 SMITH

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