(a) A firm’s profit is given by the function: Where π denotes profit, x output and y advertising expenditure.
(i) Find the profit maximizing values of x and y and hence determine the maximum profit. Confirm that the second order conditions are satisfied.
[4 marks]
(ii) If now the firm is subject to a budget constraint 2x + y = 5 determine the new values of x and y which maximize profit. [3 marks]
(b) A manufacturer determines that q units of a particular luxury item will be sold when the price is hundred shilling per unit.
(i) Find the revenue and marginal revenue functions. [3 marks]
(ii) Use marginal analysis to estimate the revenue obtained from producing the sixth unit?