Question

A company produces two types of refrigerators that use Freon gas for cooling. Each type A refrigerator sells for $2000, costs $1500 to manufacture, and leaks 15 grams of Freon. Each type B refrigerator sells for $1700, costs $1400 to manufacture, and leaks 5 grams of Freon. The following constraints exist:

1. According to environmental codes, the total average Freon leakage of all refrigerators produced in next three years must not exceed 10 grams per refrigerator.
2. Manufacturing capacity limits total refrigerator production to at most 320 during each year.
3. The demand for type A refrigerator is 100, 200, and 300 for years 1, 2, and 3, and the demand for type B refrigerator is 200, 100, and 150 for years 1, 2, and 3, respectively.
4. In order to meet a year’s demand, the company can sell either that year’s production or previous year’s production. The cost of keeping a refrigerator (type A or B) in the warehouse for one year is $200.

Formulate an LP to help the maximize its profit during the next three years. (Hint: use the following decision variables: S_ij = # of type i refrigerators sold during year j, P_ij = # of type i refrigerators produced during year j, I_ij = # of type i refrigerators in inventory at end of year j).   

Answer 1

Answer:

Given that:

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