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? 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. Maximum for 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 –3
6x + y 10
y 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? a c b d 5

What are the vertices of the feasible region determined by the constraints , , and ?
 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? 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