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jb7

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## Homework Statement

I can do most the question, but just get stuck on the final question. Here is the whole question

1. Gordon Ltd makes 2 products, Tennis racquets and badminton racquets, each using the same materials and the same skilled labour.

The costs of the products per unit of production are as follows:

......... ...Tennis...Badminton

......... ....£......£

Selling price.......... 140 .....120

Materials @ £18 per KG........9.... ...6

Labour @ £12 per hour........60..... ... 60

Other variable cost.......18... ...12

Allocation of fixed cost........ 33......22

Profit per unit.........20. ......20

The company is drawing up production plans for the 3 months to 31 March 2010. The anticipated demand in the period is for 6000 tennis racquets and 6000 badminton racquets.

There are only 4000kg of material and 50000 hours of labour available in the period.

The company has a contract to supply 1000 tennis and 2000 badminton racquets which must be satisfied. The company wishes to maximise profit in the period

(a) Formulate a linear programming model for this problem. (10 marks)

(b) Use the graphical method to determine how many doors and windows should be produced (20 marks)

(c) What are the shadow prices of materials and labour? What do these prices mean? (10 marks)

**(d) If new supplies of materials became available at £15 per kg should they be purchased? If so how much extra material should be bought? (10 marks)**

I can do up to part C, i.e calculate the shadow prices for materials and labour. However I cannot figure out how to do part D! - is it something to do with the shadow prices calculated in part C? My thoughts of how to do it was to do the WHOLE THING again, but with materials priced at £15 per kg, rather then at £18 per kg as they were initially...but something tells me that doing this incorrect. Anyone have any idea how to do this part D?

## Homework Equations

Maximise C = 53x+42y

subject to these contraints

0.5x+0.33y<=4000

5x+5y<=5000

x>=1000

y>=2000

x<=6000

y<=6000

## The Attempt at a Solution

no idea where to start with part D (don't need the solutions to the other parts.. can do them just fine thanks