Question: A company must plan its production for the next fi...

 

A company must plan its production for the next five months. The company uses, in each month, either a normal shift or an extended shift (if it produces at all). A normal shift costs $100,000 per month and can produce up to 6,000 units per month. An extended shift costs $175,000 per month and can produce up to 7,250 units per month. (For either type of shift, the cost incurred is fixed by a union guarantee agreement and so is independent of the amount produced.) It is estimated that changing from a normal shift in one month to an extended shift in the next month costs an extra $15,000. No extra cost is incurred in changing from an extended shift in one month to a normal shift in the next month.
The cost of holding stock is estimated to be $2.5 per unit per month (based on the stock held at the end of each month) and the initial stock is 4,000 units (produced by a normal shift).
The amount in stock at the end of month 5 should be zero (0) units. The demand for the company's product in each of the next five months is estimated to be as shown below:

 

Production constraints are such that if the company produces anything in a particular month it must produce at least 1,000 units. If the company wants a production plan for the next five months that avoids stockouts, formulate and solve an integer program.