Solve by linear programming (LP) - Formulation only (Setup the problem)!
variables, goal, and subject to constraints
A company has a permit to operate for five seasons. It can manufacturer only during the first four seasons and in the fifth period, it is only allowed to sell any leftover products.
It can manufacture two types of products. One unit of product 1 requires five man-hours in preparatory shop and three man-hours in finishing shop. Each unit of product 2 requires six man-hours in preparatory shop and one man-hour in finishing shop. During each season, the company has at most 1200 man-hours in preparatory and 15000 man-hours in the finishing shop (only during the first four seasons).
The product manufacturers during some season can be sold anytime from the next season onward. However, selling requires some marketing effort and it is expected that 0.1 and 0.2 man-hours of marketing effort are required to sell 10 units of products 1 and 2, respectively.
Man-hours for marketing effort can be hired at the rates given in the table at the top. There is no limit on the number of man-hours that can be hired for marketing efforts at the overtime rate.
If a unit of product is available for sale during a season, but is not sold in that season, the manufacturer has to pay carryover charges of $2 per unit to put it up for sale again in the next season. The selling prices in the various seasons are given in the table below. How should the company operate in order to maximize its total profit?
Season Normal Rate Max Man-Hrs Overtime Rate Expected Selling Price per Unit of
Per Man-Hr at Normal Rate per Man-Hour Product 1 Product 2
2 $2 400 $20 $20 $45
3 $4 300 $20 $25 $40
4 $1 600 $20 $30 $40
5 $10 1000 $20 $15 $30