Name: 
 

Linear Programming



Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1 

Find the values of x and y that maximize the objective function P = 3x + 2y for the graph. What is the maximum value?
mc001-1.jpg
a
maximum value at (5, 4); 32
c
maximum value at (9, 0); 27
b
maximum value at (0, 8); 16
d
maximum value at (0, 0); 0
 

 2 

Given the system of constraints, name all vertices. Then find the maximum value of the given objective function.
mc002-1.jpg

Maximum for mc002-2.jpg
a
(0,0), (0, 2), (2, 0), (4, 6); maximum value of –6
b
(0,0), (0, 2), (2, 0), (6, 4); maximum value of 12
c
(0,0), (0, 2), (2, 0), (4, 2); maximum value of 10
d
(0,0), (0, 2), (2, 0), (4, 6); maximum value of 8
 
 
Find the coordinates of the vertices of the figure formed by each system of inequalities.
 

 3 

y mc003-1.jpg –3
6x + y mc003-2.jpg 10
y mc003-3.jpg
10x + 3
a
(2.17, –3), (0.6, 3), (–0.44, –7.38)
b
(2.17, 7.38), (0.44, –3), (–0.6, –3)
c
(2.17, –3), (–0.6, –3), (0.44, 7.38)
d
(2.17, –3), (0.6, –3), (–3.25, 1.38)
 

 4 

Which system of inequalities best represents this graph?

mc004-1.jpg
a
mc004-2.jpg
c
mc004-4.jpg
b
mc004-3.jpg
d
mc004-5.jpg
 

 5 

What are the vertices of the feasible region determined by the constraints mc005-1.jpg, mc005-2.jpg, and mc005-3.jpg?
a
(0, 10), (0, 60), (50, 10)
c
(10, 0), (30, 30), (60, 0)
b
(10, 0), (10, 50), (60, 0)
d
(10, 50), (30, 30), (60, 0)
 

 6 

The VBC Company makes two models of office chairs. The company’s profit is $15 on each Model Q chair and $20 on each model R chair. To use linear programming to maximize profit, the company’s finance officer developed this feasible region from the constraints on the company’s resources and the pattern of demand for its products. The number of Model Q chairs to be made each week is represented by x and y represents the number of Model R chairs to be made each week. How many of each model should the company make each week in order to maximize profit?

mc006-1.jpg
a
150 model Q, 50 model R
c
100 model Q, 100 model R
b
50 model Q, 150 model R
d
0 model Q, 200 model R
 



 
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