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 at the beginning of each month and trained

immediately at a cost of $$5000$ per worker. Workers can be laid off at the beginning of each month

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. How many workers should be hired or laid off at the BEGINNING OF EACH MONTH?