economic function problem

A manufacturer of small glass figurines discovers that it costs 2300 for a production run of 2000 . Assuming that cost is a linear function of the number of items, find the overhead and the marginal cost of a figurine.

Answers
1) Let's call the cost of a figurine "c" and the overhead "h" 2) Then if a production run of 1100 costs £1500 we have the equation: 1100c + h = 1500 ----(a) 3) If a run of 2000 costs £2300 then we have the equation: 2000c + h = 2300 -----(b) 4) subtracting equation (a) from equation (b) gives 2000c+h-1100c-h=2300-1500 which simplifies to 900c=800 5) Dividing both sides of this equation by 900 gives c=800/900=0.889 (So the cost of a figurine is 89p) 6) We can now use this answer in equation a) so 1100*0.889 + h = 1500 so 977.9 + h = 1500 so h = 1500 - 977.9 = 522.1 so the overhead cost is £522.10 Answer: cost of figurine: 89p overhead: £522.10
mike_jory
23 September 2012
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