Use graphical methods to solve the linear programming problem.
25)
Minimize z = 2x + 4y
subject to: x + 2y
10
3x + y
10
x 0
y 0
25)
A)
Minimum of 20 when x = 2 and y = 4, as well as when x = 10 and y = 0, and all points in
between
B)
Minimum of 20 when x = 10 and y = 0
C)
Minimum of 0 when x = 0 and y = 0
D)
Minimum of 20 when x = 2 and y = 4
26)
Minimize z = 4x + 5y
subject to: 2x – 4y 10
2x + y
15
x 0
y 0
26)
A)
Minimum of 39 when x = 1 and y = 7
B)
Minimum of 20 when x = 5 and y = 0
C)
Minimum of 33 when x = 7 and y = 1
D)
Minimum of 75 when x = 0 and y = 15
Solve the problem.
27)
The Old–World Class Ring Company designs and sells two types of rings: the BRASS and the
GOLD. They can produce up to 24 rings each day using up to 60 total man–hours of labor. It takes 3
man–hours to make one BRASS ring and 2 man–hours to make one GOLD ring. How many of each
type of ring should be made daily to maximize the company’s profit, if the profit on a BRASS ring
is $40 and on an GOLD ring is $30?
27)
A)
10 BRASS and 14 GOLD
B)
12 BRASS and 12 GOLD
C)
14 BRASS and 14 GOLD
D)
14 BRASS and 10 GOLD
Use graphical methods to solve the linear programming problem.
28)
Maximize z = 6x + 7y
subject to: 2x + 3y 12
2x + y
8
x 0
y 0
28)
A)
Maximum of 52 when x = 4 and y = 4
B)
Maximum of 32 when x = 3 and y = 2
C)
Maximum of 24 when x = 4 and y = 0
D)
Maximum of 32 when x = 2 and y = 3
Graph the inequality.
29)
4x + y -6
29)
16
A)
B)
C)
D)
Define the variable(s) and translate the sentence into an inequality.
30)
Sales of wheat bread are at least $2000 greater than sales of white bread.
30)
A)
Let e = wheat bread sales; let i = white bread sales; w i + $2000
B)
Let e = wheat bread sales; let i = white bread sales; w + i $2000
C)
Let e = wheat bread sales; let i = white bread sales; i w + $2000
D)
Let e = wheat bread sales; let i = white bread sales; w
i + $2000
Use graphical methods to solve the linear programming problem.
31)
Suppose an horse feed to be mixed from soybean meal and oats must contain at least 100 lb of
protein, 20 lb of fat, and 9 lb of mineral ash. Each 100–lb sack of soybean meal costs $20 and
contains 50 lb of protein, 10 lb of fat, and 8 lb of mineral ash. Each 100–lb sack of oats costs $10 and
contains 20 lb of protein, 5 lb of fat, and 1 lb of mineral ash. How many sacks of each should be
used to satisfy the minimum requirements at minimum cost?
31)
A)
0 sacks of soybeans and 2 sacks of oats
B)
13
11 sacks of soybeans and 19
11 sacks of oats
C)
7
3 sacks of soybeans and 5
6 sacks of oats
D)
2 sacks of soybeans and 0 sacks of oats
Graph the solution set of the system of linear inequalities and indicate whether the solution region is bounded or
unbounded.
32)
x –4
y > 2
3x + y < 6
32)
A)
Unbounded
B)
Bounded
18
C)
Bounded
D)
Unbounded
Define the variable(s) and translate the sentence into an inequality.
33)
Enrollment is below 8000 students.
33)
A)
Let e = student enrollment; e
8000
B)
Let e = student enrollment; e < 8000
C)
Let e = student enrollment; e 8000
D)
Let e = student enrollment; e > 8000
Graph the solution set of the system of linear inequalities and indicate whether the solution region is bounded or
unbounded.
34)
y–3x –3
yx +6
34)
19
A)
Unbounded
B)
Unbounded
C)
Unbounded
D)
Unbounded
Graph the constant–profit lines through (3, 2) and (5, 3). Use a straightedge to identify the corner point(s) where the
maximum profit occurs for the given objective function.
35)
P = 5x + y
35)
A)
Max P = 45 at x = 9 and y = 0, at x = 8 and y = 4, and at every point on the line segment joining
the preceding two points.
B)
Max P = 44 at x = 8 and y = 4
C)
Max P = 45 at x = 9 and y = 0
D)
Max P = 44 at x = 8 and y = 4, at x = 0 and y = 12, and at every point on the line segment
joining the preceding two points.
Graph the inequality.
36)
4x – 2y 8
36)
21
A)
B)
C)
D)
37)
A salesperson has two job offers. Company A offers a weekly salary of $180 plus commission of 6%
of sales. Company B offers a weekly salary of $360 plus commission of 3% of sales. What is the
amount of sales above which Company A’s offer is the better of the two?
37)
A)
$12,000
B)
$6100
C)
$3000
D)
$6000
Graph the constant–profit lines through (3, 2) and (5, 3). Use a straightedge to identify the corner point(s) where the
maximum profit occurs for the given objective function.
38)
P = x + y
38)
A)
Max P = 8 at x = 5 and y = 3
B)
Max P = 5 at x = 3 and y = 2
C)
Max P = 9 at x = 9 and y = 0, at x = 8 and y = 4, and at every point on the line segment joining
the preceding two points.
D)
Max P = 12 at x = 0 and y = 12, at x = 8 and y = 4, and at every point on the line segment
joining the preceding two points.
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Answer Key
Testname: C5
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Answer Key
Testname: C5
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Answer Key
Testname: C5