A company produces two goods, labelled as A and B.

Its total costs are: TC= 5QA + 20QB + QAQB

Where QA represents the quantity produced of good A and QB the quantity produced of good B. The inverse demand functions for good A and B are, respectively:

PA= 40 - QA

PB= 40 - 1/3 QB

Where PA and PB represent the price of good A and B, respectively.

(a) Use partial differentiation to find the output quantities of good A and B that maximise the firm's profit. [6 marks]

(b) Find the prices the firm should charge. [1 mark]

(c) Find the maximum profit. [1 mark]

(d) Use second order conditions to check that your answer to part (a) is a maximum. [3 marks]

(e) Find marginal revenue and marginal cost for each good. Are the two goods complements, substitutes or independent in production? How about in consumption? Briefly explain.