Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 3

A canning company produces two sizes of cans-regular and large. The cans are produced in 10,000-can lots. The cans are processed through a stamping operation and a coating operation. The company has 30 days available for both stamping and coating. A lot of regular-size cans requires 2 days to stamp and 4 days to coat, whereas a lot of large cans requires 4 days to stamp and 2 days to coat. A lot of regular-size cans earns $800 profit, and a lot of large-size cans earns $900 profit. In order to fulfill its obligations under a shipping contract, the company must produce at least nine lots. The company wants to determine the number of lots to produce of each size can ( x 1 and x 2 ) in order to maximize profit.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis.