Hi, I've been having trouble formulating the following problem, if someone could show me the appropriate constraints and objective function, would be much appriciated
Deckmaster builds decks using student employees during the summer months of June, July, and August. The company projects that it will receive the following number of calls from people who want decks built: 100 calls in June, 300 calls in July, and 200 calls in August. Deckmaster is paid $800 for deck that is built 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 Deckmaster loses $100 in future goodwill, and if a call is responded to two months after it is made, Deckmaster loses $200 in goodwill. Each employee of Deckmaster can build 10 decks during a month. Each employee is paid a salary of $4000 per month. At the beginning of June, the company has 8 workers. Workers can be hired and trained immediately at a cost of $5000 per worker. Workers can be fired at a cost of $4000 per worker. Fractions of workers are permitted by using part-time employees.
Formulate an LP to maximize Deckmaster profits over the next 3 months. Assume that all decks requested must be built by the end of August.