Shoetec Ltd., a manufacturer of stylish shoes, estimates that at full scale production, it would sell between 2,000 and 3,000 pairs of shoes.
The total monthly revenue in thousands of shillings over this range is represented by the function
TR = 3x²+7x.
The firm estimates that the marginal cost (MC) in thousands of shillings could be represented by the function
MC = 5x2-3x-2 and fixed cost (FC) will be Sh.1,000 per month.
Where x is the monthly output in thousands of pairs of shoes.
Required:
(i) Derive the average cost and average revenue functions of the firm.
(ii) Calculate the profit maximising output.
(iii) Calculate the price charged upon maximizing profit and how much each pair of shoes would cost.
(2 marks)