Chargers-are-us bakery makes pumpkin pies and cinnamon apple cider donuts during
November of each year. During any week, they can bake at most 65 pumpkin pies and 90
donuts. The costs and the demands for pies and donuts, which must be met on time, are listed
in the Table. It costs $1 to hold a pumpkin pie, and 50¢ to hold a cinnamon apple cider donut,
in inventory for a week. At the end of the 4 weeks, there should not be any pumpkin pies or
donuts left at the store.
Pumpkin pie Cinnamon apple cider donut
Week 1 Demand 60 75
Cost ($ per item) 3 2
Week 2 Demand 70 50
Cost ($ per item) 3.4 2.8
Week 3 Demand 45 100
Cost ($ per item) 3.2 2.5
Week 4 Demand 75 85
Cost ($ per item) 3.1 2.7
a) (60 points) Formulate a linear programming model to minimize the total cost of meeting
the next four weeks’ demands. To receive the full points of this part, you need to provide
definitions of all of the variables and explain the objective function as well as all of the
constraints. Simply writing the mathematical formula will not be sufficient.
b) (35 points) Solve the linear program using the IBM ILOG CPLEX Optimization Studio.
You need to interpret the results and your findings to receive the full points of this part.
Copying the result of the CPLEX is not sufficient.
c) (5 points) How would your objective function change if you want to minimize the total
cost of inventory?