The T. E. Callarman Appliance Company is thinking of manufacturing and selling t

Question

The T. E. Callarman Appliance Company is thinking of manufacturing and selling trash compactors on an experimental basis over the next 6 months. The manufacturing costs and selling prices of the compactors are projected to vary from month to month. It cannot sell any compactors in July and it does not manufacture any compactors in December. The following table gives these forecast costs and prices. Month Manufacturing Cost Selling Price (During Month Uul August September October November December $60 $60 $50 $60 $70 $80 $70 $80 90 All compactors manufactured during any month are shipped out in one large load at the end of that month. The firm can sell as many as 300 units per month, but its operation is limited by the size of its warehouse, which holds a maximum of 100 compactors. Callarman has no compactors on hand (inventory) at the beginning of July and wishes to have no compactors on hand (inventory) at the end of the test period in December Callarman's operations manager, Richard Deckro, needs to determine the number of compactors to manufacture and sell each month to maximize the firm's profit. a) Formulate this problem as an LP model. b) Solve the problem by Excel. What is the maximum profit that Callarman can achieve?

Explanation / Answer

To formulate this LP problem

Number of units manufactured in the months= A1 , A2, A3,A4,A5,A6

Number of units sold in the given months= B1,B2,B3,B4,B5,B6

As the company starts with no compactors in the first month so no sales are done in that period

And it requires zero inventories in the December so manufacturing in December month must be zero.

Maximize profit= (80B2+60B3+70B4+80B5+90B6)- (60A1+60A2+50A3+60A4+70A5)

Now to set up constraints, deckro needs to introduce new set of variables which represent inventories at the end of the month. I1,I2,I3,I4,I5,I6

Inventory at the end of this month= inventory at the end of the previous month+ current month production- month sales

For july month I1=A1 as there was no sale

For august month I2= I1+A2-B2

Likewise for the coming months same procedure

The final solution yield a profit of $19000

A1=100 , A2= 200, A3=400,A4= 300, A5=300, A6=0

B1=100, B2=300, B3=300,B4=300,B5=300, B6=0

I1= 100, I2= 0, I3=100, I4=100,I5=100,I6=0

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