Ghostbusters, Inc., exorcises (gets rid of) ghosts. During each of the next three months, the company will receive the following number of calls from people who want their ghosts exorcised: January, 100 calls; February, 300 calls; March, 200 calls. Ghostbusters is paid $800 for each ghost exorcised during the month in which the customer calls. Calls need not be responded to during the month they are made, but if a call is responded to one month after it is made, then Ghostbusters loses $100 in future goodwill, and if a call is responded to two months after it is made, Ghostbusters loses $200 in goodwill. Each employee of Ghostbusters can exorcise 8 ghosts during a month. Each employee is paid a salary of $4,000 per month. At the beginning of January, the company has 10 workers. Workers can be hired and trained (in 0 time) at a cost of $5,000 per worker. Workers can be fired at a cost of $4,000 per worker.
a. Formulate an LP to maximize Ghostbusters’ profit (revenue less costs) over the next three months. Assume that all calls must be handled by the end of March (Ignore any integer restrictions).
b. Use LINDO/LINGO (or other LP solver) to find the optimal solution and describe it briefly in “plain English”. Are integer numbers of workers hired & fired?
c. Add integer restrictions to the formulation in part (a), and solve using LINDO/LINGO (or other LP solver). Compare the new optimal solution with the one in part (b). What has been changed?
A manufacturer can sell product 1 at a profit of $3/unit and product 2 at a profit of $4/unit. Three units of raw material are needed to manufacture 1 unit of product 1, and 6 units of raw material are needed to manufacture 1 unit of product 2. A total of 120 units of raw material are available. If any of product 1 is produced, a setup cost of $10 is incurred, and if any of product 2 is produced, a setup cost of $15 is incurred. Formulate an IP to maximize profits, and solve using
the optimal solution briefly in “plain English”.