Ghostbusters, Inc., exorcised (gets rid of) ghosts. During each of the next thre

Question

     Ghostbusters, Inc., exorcised (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: Jan 100 calls, Feb 300, Mar 200. 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 looses $100 in future goodwill, and if a call is responded to two months after it is made,Ghostbusters looses $200 in future goodwill. Each employee of Ghostbusters can exorcise 10 ghosts during a month. Each employee is paid a salary of $4000 per month. At the beginning of January, the company has 8 workers. Workers can be hired and trained (in 0 time) at a cost of $5000 per worker. Workers can be fired at a cost of $4000 per worker. Formulate an LP to maximize Ghostbusters profit (revenue less costs) over the next months. Assume that all calls must be handled by the end of March

I need to have immediately Lindo or Excel solver solution please

Explanation / Answer

Let us assume that

Di = calls received in month i

Si =the calls serviced in month i

Bi = the calls which are still yet be attended in end of month i

So

Bi=Bi-1 +Di –Si

Now let us assume the following:-

Xi = the calls which were responded in month i but were received prior to one month

Yi = the calls made which were responded in month i but received prior to two months

So

Xi +Yi ? Si

Xi +Yi= Bi-1

Let us consider that

Wi = the workers working in month i

In the question

Si =10 Wi

Hi = workers hired in month i

Fi = the workers fired in month i

So ,

Wi = Wi-1 +Hi –Fi

The main objective of the case is to reduce the total cost

So we can formulate the problem as below

C= Min ?( 100 Xi +200Yi +400 Wi +5000 Hi +4000 Fi)

Subject to:-

Bi= Bi-1 +Di -Si

Xi +Yi ? Si

Xi +Yi= Bi-1

Si =10 Wi

Wi = Wi-1 +Hi –Fi

W1=8

B0=0

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