MATH 318, Chapter 8 Quiz

Name:
You may use a calculator on this quiz. You may not use a cell phone or computer. Please read each question carefully, show your work and give justifications for your answers. If you find that you are spending a lot of time on one problem, leave it blank and move on to the next. There are questions on both sides of this quiz paper.
1. (50 points) Suppose you're the owner of a souvenier shop in Plymouth. You're trying to decide how many umbrellas and how many baseball hats to purchase in your monthly order. You believe the optimal amounts are determined by the linear programming problem formulated below, where U is the number of umbrellas purchased, H is the number of hats purchased, and the feasible region is shown on the right.

 Max. 4U + 3H S.t.: U < 70 H < 60 2U - H < 100 U, H > 0

a) How many hats should you order? How many umbrellas?

b) Suppose you realize that you've made an error in your calculations and that the constraint 2U - H < 100 should actually be 2U + H < 100. Will this affect the feasible region? If so, how?

c) If you could pay \$1.00 per unit to change the right hand side of the constraint 2U - H < 100 would you increase it, decrease it or leave it the same? (Example: pay \$10 to change the equation to 2U - H < 90.)

d) If you could pay \$1.00 per unit to change the right hand side of only one of the three constraints, which would you change and how?

e) If you had to pay \$5.00 per unit to make the change you suggested in part (d) and that change affected only this order, would you still make that change? Why or why not?

2. (30 points) Fill in each of the blanks below with the letter of an appropriate phrase:

a) Changing the coefficient of a constraint function
b) Changing the coefficient of the objective function
c) Changing the right hand side of a constraint

___________ changes the slope of the line of constant profit/cost.

___________ may change the slope of a side of the feasible region.

___________ may move a side of the feasible region parallel to itself.

3. (20 points) True or False: Changing the right hand side of a constraint function always changes the shape of the feasible region. Explain your answer.