The Monkey Bagels Biscuit Company produces Crackers, Cookies and Bagels. It has outlets in Jersey and York. It is the company's policy that its production must satisfy the demand at the outlets. The monthly demand for the products (in thousand pounds) are:
Jersey York
Crackers 20 30
Cookies 50 25
Bagels 30 20
The company has two production facilities, one in Cranium and one in Medulla. Each facility can make each product.
Production involves two key operations ---baking and packing. The oven capacity at the Cranium and Medulla bakeries are, respectively, 150 and 100 thousand pounds (of raw ingredients fed in) per month. Each facility uses its own packing line, which packs the Crackers and Bagels that it bakes. Cookies are shipped in bulk; they need not be packed. The capacities of the packing lines in Cranium and Medulla are, respectively, 80 and 50 thousand pounds per month. This capacity is measured in the quantity processed through the packing line.
The baking line in Cranium is not automated, and an agreement has been reached with the Cranium workers that at least 25 percent of its baking (as measured by oven usage) must be devoted to Cookies, which are more labor intensive than Crackers and Bagels.
The shipping cost is the same for all products. The cost (in dollars) per thousand pounds shipped from the bakeries to the outlets is given below:
Jersey York
Cranium 15 30
Medulla 20 10
The production costs (in dollars per thousand pounds of raw ingredients fed) are:
Cranium Medulla
Crackers 5 4
Cookies 6 7
Bagels 5 5
The Operations Manager of the Monkey Bagels Biscuit Company must design a production/distribution plan so that the total monthly costs --- manufacturing and transportation costs --- are as low as possible.
The Operations Manager must decide how much of each product to manufacture at each bakery and how much to ship to each outlet.
(a) Formulate a linear program to solve this problem. Define your decision variables and explain the constraints.
(b) Solve the linear program.