## Formulating a linear programming problem

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.

### Formulating a linear programming problem

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.
winnerchickendinner

Posts: 2
Joined: Mon Oct 14, 2013 11:56 pm

### Re: Formulating a linear programming problem

so this is what i know,

decks to be built (calls)
100 in june
300 in july
200 in august

\$800 / deck when built in mo when customer calls
-\$100 / if call answered 1 mo late
-\$200 / if call answered 2 mo late

Each employee

10 decks / mo
\$4000 salary / mo

in june
8 workers

hired/trained immediately
\$5000 / worker

fired
\$4000 / worker
*fraction of a worker allowed

now what?
winnerchickendinner

Posts: 2
Joined: Mon Oct 14, 2013 11:56 pm

### Re: Formulating a linear programming problem

A good start is probably to figure out what you need to find, and in what terms. Would it be helpful to state things in terms of variables for the months? For the employees? Or for something else? Have you tried setting things up for just one of the three months, to see if this gives you any ideas on how to proceed for the whole summer?

maggiemagnet

Posts: 289
Joined: Mon Dec 08, 2008 12:32 am