33)
Sketch the region described by the inequalities
2x+y 1
x–y
1
33)
34)
Find the dual problem to the following: A company has two different locations to assemble
three different models of PCs. The table below summarizes the daily production capacity,
the minimum number of each type needed, and the daily operating costs for each location.
What is the number of days that each location needs to operate in order to fill the orders at
minimum cost.
Location 1 Location 2 Min. Number
Model 1 60/day 60/day 2400
Model 2 40/day 80/day 2000
Model 3 60/day 40/day 1800
Weekly Cost $16,000 $12,000
34)
35)
Maximize
Z= 10x+ 15y
subject to
x+ 3y
15
4x + 3y
24
x 0, y 0
35)
36)
Maximize
Z = 5x– 3y
subject to
2x–y
8
2x– 5y
0
x –y= – 2
x, y 0.
36)
37)
Maximize
Z= 4x + 6y
subject to
x + y 3
y 5
x 4
x 0, y 0
37)
38)
Use the simplex method to
maximize
Z =x1+ 4x2+x3
subject to
x1+x2+x3 6
x1–x2–2x3 2
x1, x2, x3
0 .
38)
39)
Use the dual and the simplex method to
minimize
Z = 4x1+ 5x2
subject to
x1–x24
2x1–x21
5x1+ 3x23
x1, x20.
39)
40)
Suppose a car dealer has showrooms in Atherton and Berkeley and warehouses in Concord
and Dublin. The cost of delivering a car is $60 from Concord to Atherton, $45 from
Concord to Berkeley, $50 from Dublin to Atheron, and $35 from Dublin to Berkely.
Suppose that the showroom in Atherton orders 7 cars and the showroom in Berkeley
orders 4 cars. Also suppose that the warehouse in Concord has 8 cars and the warehouse in
Dublin has 6 cars available. Find the best way to minimize cost and find the minimum cost.
(Hint: Let x1 be the number of cars delivered from Concord to Atherton and x2 be the
number of cars delivered from Concord to Berkeley. Thus 7 –x1 is the number of cars
delivered from Dublin to Atherton and 4 –x2 the number of cars shipped from Dublin to
Berkeley.)
40)
41)
Use the simplex method to minimize
Z = – x1+ 2x2
subject to
x1+x2 4
5x1+x2–12
2x1+ 5x2–14
3x1– 2x2 17
41)
42)
Maximize
Z = 2x– 3y
subject to
2x+y1
x –y1
x, y0.
Also find the corner point where the value of z is attained.
42)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the inequality.
43)
4x– 2y4
43)
A)
B)
C)
D)
44)
x–y> – 3
44)
A)
B)
C)
D)
45)
x+y–2
45)
A)
B)
C)
D)
19
46)
2x– 3y6
46)
A)
B)
C)
D)
47)
A summer camp wants to hire counselors and aides to fill its staffing needs at minimum cost. The
average monthly salary of a counselor is $2400 and the average monthly salary of an aide is $1100.
The camp can accommodate up to 45 staff members and needs at least 30 to run properly. They
must have at least 10 aides, and may have up to 3 aides for every 2 counselors. How many
counselors and how many aides should the camp hire to minimize cost?
47)
A)
27 counselors and 18 aides
B)
18 counselors and 12 aides
C)
12 counselors and 18 aides
D)
35 counselors and 10 aides
48)
Use the simplex method to:
minimize
Z = 3x1+ 2x2
subject to:
x1+7x22
2x1+x27
7x1+9x21
x1, x2 0
48)
A)
Z = 14 when x1= 0, x2= 7
B)
Z = 14 when x1= 7, x2= 0
C)
Z = 21 when x1= 7, x2= 0
D)
Z =21
2 when x1=7
2, x2= 0
Solve the inequality.
49)
4x+y> – 2
49)
21
A)
B)
C)
D)
22
23
Answer Key
Testname: C7
24
Answer Key
25
Answer Key
Testname: C7