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?

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