May 2017 Q3

a) The AXM manufacturing company has determined that the cost function for producing a particular type of pavement block is given by:

where x is measured in number of units and C(x) in GH¢.

Required:
i) Calculate the derivative of C(x) with respect to x .                                                                                                          (5 marks)

ii) Determine how quickly the cost is changing at x =1000.                                                                                               (4 marks)

b) At the Zee manufacturing company, the marginal cost for producing x gears, measured in hundreds is

MC =10+0.1x .
If the fixed cost (the cost of producing zero items) is GH¢3000.
Required:
Determine the cost for manufacturing 5000 gears.                                                                                                            (11 marks)