# MATHEMATICS

1. Identify the feasible region for the following set of constraints:

3x 2y 0 2x y 200 x 150

x,y 0

2. Given the linear program

Max 3x ￼ 4y

s.t. x 2y 8

x 2y 12 2x y 16 x,y 0

Summer 2014

a. Write the problem in standard form. Identify slack/surplus variables.

b. Solve the problem using the graphical solution procedure.

c. What are the values of the three slack/surplus variables at the optimal solution?

3. Consider the following LP problem:

Maximize Profit 5x ￼ 6y Subjectto 2x y 120

2x 3y 240 x,y 0

a. Solve this problem using Excel Solver. Provide answer report and sensitivity report.

b. What is the optimal solution to this problem?

c. If a technical breakthrough occurred that raised the profit per unit of x to $8, would this affect the optimal solution?

d. If the profit per unit of x was overestimated and only should have been $4.5 but the profit per unit of y was underestimated and should have been $6.5, would this affect the optimal solution?

e. If the right-hand side of constraint 1 were increased by 1 unit, how would the profit change?

f. If the right-hand side of constraint 2 were increased by 1 unit, how would the profit change?

g. If you were to choose to increase the right-hand side by 1 unit for one constraint, which constraint would you choose?