Ashley's manufactures home furnishings for department stores. Planning is underway for the production of the following items during the next production period:
Quilts (x1) Blinds (x2) Pillows (x3)
Fabric required (yards) (d1) 7 4 9
Time required (hours) (d2) 1.5 2 0.5
Packaging material (ounces) (d3) 3 2 1
Profit (d4) 12 10 8
Ashley has 3000 yards of material in stock for this production period. Five hundred hours of production time are scheduled and 400 ounces of packaging material is available. Each of these quantities can be adjusted through overtime or extra purchases. Ashley's highest priority is to achieve a profit of $3200. Her second priority is to avoid additional purchases of packaging material. Third, she wants to use all of the scheduled production hours, and fourth, minimize any fabric remaining from the 3000 yards. Note that the deviational variables associated with each item are given in the table. (20 points)
a. What is the objective function?
b. What is the fabric constraint?
c. What is the production time constraint?
d. What is the packaging material constraint?