Linear programming

Durham Designs manufactures home furnishings for department stores. Planning is underway for the production of items in the "Wildflower" fabric pattern during the next production period.

Bedspread Curtains Dust Ruffle
Fabric required (yds) 7 4 9
Time required (hrs) 1.5 2 .5
Packaging material 3 2 1
Profit 12 10 8

Inventory of the Wildflower fabric is 3000 yards. Five hundred hours of production time have been scheduled. Four hundred units of packaging material are available.
Each of these values can be adjusted through overtime or extra purchases.

Durham has the following goals:
Priority 1:
 Achieve a profit of $3200,
Priority 2:
 Avoid purchasing any more fabric or packaging material than is available, and
 Use all of the hours scheduled.

Give the goal programming model, then solve and report the solution.
Formulation: