QUESTION 3 [10 Marks] TC =4+97q- 8.5q2 +_ 3.1 Given a total cost function: Determine the level of output where marginal cost (MC) is a minimum. Prove that this point is a minimum. [2] 3.2 A firm is selling two goods, x and y, with a total profit function: TP =- 13.7+60x + 60y - 0.07x2 - 0.08y2 - 0.08xy Find the values of x and y that will maximise profit. Prove that profit is a maximum. [4] 3.3 A monopolistic producer produces two goods, G1 and G2, with a joint total cost function: TC=10Q,+Q,Q2+10Q2 Q1=Quantity of G1 Q2=Quantty of G2 and a joint total income function: TR=50Q,-Q;+3Q,Q2+30Q2-Q3 Use Lagrangian multipliers to determine the maximum profit this firm can make subject to the constraint: Q1+Q2=15 [4]