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Where P is price and Q is total output in the market (in thousands). For simplicity, also assume that both firms produce an identical product,

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Where P is price and Q is total output in the market (in thousands). For simplicity, also assume that both firms produce an identical product, have no fixed costs, and marginal cost MC = MCy= $140. i. Derive the output reaction curves for firms X and Y. ii. Calculate the Cournot market equilibrium price and output solutions. ili. Calculate the total revenue for firm X. QUESTION 6 A firm manufactures two types of juices - sweetened and unsweetened. The profit contribution for each product is: $300 per sweetened and $12 per unsweetened. Both products are processed on three machines - M1, M2 and M3. The time required for each product and the total time available per week on each machine is as follows: Sweetened Unsweetened Machine Available Hours per (Hours) (Hours) Week M1 H 11 M2 1 N 27 M3 2 5 90 a. Write down the objective function and all the constraints. b. Write down the initial tableau required by the Simplex Method. c. Use the Simplex Method, to solve the linear programming problem and interpret the solution values.A. The total cost function of a firm under perfect competition is given by TC = 540,562.5 + 40Q + 0.025Q2 and the demand function is P = 412 - 0.03Q per unit of output. What is the profit maximising level of output? (6 marks) ii. Calculate the profit maximizing price. (2 marks) iii. Calculate total profit at the profit maximising level of output. (3 marks) B. The total cost function for a company, which manufactures MP3 players is estimated to be TC = 100 + 20Q - 602 + 0.2503. The price of each device is $$80. i. Should the owner close the outlet? Explain! (6 marks) C. Given the information in the table about the demand for a certain product estimate: Quantity Price 180,000 96 320,000 64 i. the demand function (5 marks) ii. the demand curve (2 marks) ili. the revenue maximizing quantity (4 marks) iv. the revenue maximizing price (2 marks)

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