A canning company produces two sizes of cans-regulars 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 20 days available for both stamping and coating. A lot of regular-size cans require 3 days to stamp and 5 days to coat, whereas a lot of large cans requires 4 days to stamp and 3 days to coat. A lot of regular-size cans earns $1200 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 (x1 and x2) in order to maximize the profit.

Set up the problem as an LP:

Define the variables

Define the objective function

Define the constraints