An electronics firm carries out a small-scale test launch of a new low-priced
pocket calculator. It estimates from this test that if it went into full-scale
production it would sell between 1,000 and 2,500 calculators per month, and
that is monthly revenue in thousands of shillings over this range of sales could
be represented by the equation:
R = -x2 + 5x
where: x is the monthly output in thousands of calculators (it is assumed that it
sells its entire output).
From experience of calculator production, the firm estimates that its marginal
costs in thousands of shillings could be represented by the equation:
MC = x2 – x + 2
and that its fixed costs will be Sh. 500 per month.
(i) Determine the average cost and revenue equations for this firm. (4
(ii) Determine the profit-maximizing output, the price that should be
charged to maximize profit, and how much each calculator will then cost