Question 3 Assume that the quantities of two products (A and B) produced by a multi-product firm are given by the functions Qa = 10PB – 10PA. QB = 100 + 10PA – 20Pn. where Qa, QB, PA and Pg denote respectively, the quantity of A produced, the quantity of B produced, the price per unit (in dollars) of A, and the price per unit (in dollars) of B. The average cost of producing one unit of A is $1, and the average cost of producing one unit of B is $2. (1) Derive the total profit of the firm as a function of Pa and Pg. (2) Find Pa and Pg that maximise the firm's total profit. (3) Calculate quantity values of Qa and Qp at the prices that maximises the firm's total profit.

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