(a) A manufacturer of jet engines estimates that the rate at which maintenance costs are incurred on its

engines is a function of the number of hours of operation of the engine. For one engine used on

commercial aircraft, the function is

7(x) = 60+0.040x

where x equals the number of hours of

operation and

operation.

r(x)

equals the rate at which repairs cost are incurred in dollars per hour

of

. Determine the rate at which costs are being incurred after 100

hours of operation. [2 Marks] ii. What are the total costs expected to equal during the first 100

hours of operation. [3 Marks] (b) The cost accountant of a firm

producing colour television has worked out the total cost function for the firm as TC = 1200-02 +0.020. A sales manager has provided the sales forecasting function

as P=114-0.250

where P is price and the quantity sold. Required: - i. Find the level of production that will yield minimum

average cost per unit and determine whether this level of output maximizes profit for the firm.

Marks]

[10

ii.

Determine the price that will maximize profit for the

firm.

[2 Marks]

Determine the maximum revenue for this firm.

[3

Marks]