CH4 Solutions

CH4 Solutions - 306-310 ENGINEERING ECONOMY SOLUTIONS TO...

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1 3 0 6 - 3 1 0 E N G I N E E R I N G E C O N O M Y SOLUTIONS TO PROBLEM SET #4 – PRODUCTION AND COST ANALYSES 1. i) The total cost function consists of two linear segments intersecting at a rate of 500 units per week. Let L represent the number of person-hours of labour employed per week. The mar- ginal cost function is: For L 500: MC = 20 (also vc because of the linear cost function) For L 500: MC = 30 At the current production rate, the total production costs are: 400 (50) = 20 000 Therefore, the fixed cost is: 20 000 - 400 (20) = 12 000 The total production cost function is: For L 500: TC = 12 000 + 20 (L) For L 500: TC = 12 000 + 20 (500) + 30 (L - 500) = 7000 + 30 L Therefore, the average cost function is: For L 500: AC = 12 000 / L + 20 For L 500: AC = 7000 / L + 30 The marginal and average cost curves are shown in the diagram below. 0 20 40 60 80 100 120 140 160 180 200 0 100 200 300 400 500 600 700 800 900 1000 PRODUCTION RATE (units/week) UNIT COSTS ($) Average Cost Marginal Cost
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2 ii) As determined above, the fixed cost of the process is $12 000 per week . iii) Given a selling price of $40 per unit and an average cost of $50, the operation is not viable at the current production rate of 400 units per week. As the marginal costs of $20 and $30 are lower than the selling price, the break-even production rate occurs at a rate above the current production rate. A viable operation will be achieved when the production rate exceeds that break-even rate, which is determined as follows: At the break-even rate, TR=TC. Assuming first that the break-even rate is below 500 units per week, we have: TR = 40 L TC = 12 000 + 20 L At the break-even rate L*, we have: 40 L * = 12 000 + 20 L * This relationship is satisfied at L * =600. Since the total cost function used is that which is associ- ated with a production rate below 500 units, the solution obtained here is unsatisfactory, and hence, the break-even rate must be above 500 units per week. Therefore, we have: 40 L * = 7000 + 30 L * This relationship is satisfied at L * =700. To be viable, the shop must handle more than 700 ser- vice units per week. Each unit of service sold above the 700-unit limit generates a profit of $10, i.e. the contribution margin. Thus, a production rate of 900 units would generate a profit of $2000. Therefore, the production rate should be as high as possible, as long as demand for the service exists and production remains within the physical limits of the shop facility. 2. i) For linear cost functions, the break-even production rate (Q * ) is determined from the following relationship: Q * = FC / (p - vc) in which FC represents the fixed cost, p, the unit selling price, and vc, the constant unit (average) variable costs. a)
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This note was uploaded on 10/06/2009 for the course MIME 310 taught by Professor Bilido during the Summer '08 term at McGill.

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CH4 Solutions - 306-310 ENGINEERING ECONOMY SOLUTIONS TO...

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