solutions to tutorial 4

solutions to tutorial 4 - 1 McGill Faculty of Engineering...

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Unformatted text preview: 1 McGill Faculty of Engineering MIME 310 Engineering Economy Tutorials Chapter 4. Production and Cost Analyses 2 McGill Faculty of Engineering MIME 310 Engineering Economy Tutorials 4.1 The total annual cost (TC) of pumping potable water to a small community is given by: TC = 200 000 + 0.8 V 1.3 in which TC is given in dollars per year and V, the volume of water pumped, in m 3 /day. i) TC @ 4000 m 3 /day: 200 000 + 0.8 (4000) 1.3 = 200 000 + 38 527 = 238 527 \ AC = 238 527 / [4000 (365)] = $0.163/m 3 or AC = 200 000 / V + 0.8 V 0.3 Units: ($/yr) / (m 3 /day) or $ / 365 m 3 = 200 000 / 4000 + 0.8 (4000) 0.3 = 50 + 9.632 = $59.632 / 365 m 3 = $0.163/m 3 Determine: i) The average cost for a volume of 4000 m 3 /day; ii) The marginal cost at a volume of 4000 m 3 /day. 3 McGill Faculty of Engineering MIME 310 Engineering Economy Tutorials ii) MC = dTC/dV = 1.04 V 0.3 Units: ($/yr) / (m 3 /day) or $ / 365 m 3 Alternate solution: TC @ 4000 m 3 /day: 200 000 + 0.8 (4000) 1.3 = 238 527.247 TC @ 4001 m 3 /day: 200 000 + 0.8 (4001) 1.3 = 238 539.769 Difference $12.522 for 365 m 3 = 1.04 (4000) 0.3 = $12.521 / 365 m 3 = $0.034/m 3 4 McGill Faculty of Engineering MIME 310 Engineering Economy Tutorials 4.2 Consider the following total revenue (TR) and cost (TC) functions: TR = 350 Q - 0.025 Q 2 TC = 200 000 + 130 Q - 0.005 Q 2 in which TR and TC are given in dollars per period and Q, in units per period. i) At break-even, TP = TR - TC = 0 TP = 350 Q - 0.025 Q 2- [200 000 + 130 Q - 0.005 Q 2 ] = -0.02 Q 2 + 220 Q - 200 000 = (-0.2 Q + 200) (0.1 Q - 1000) ... by factoring Determine: i) The break-even production rate; ii) The rate at which the profit per period is maximised. 200 400 600 800 1000 1200 1400 2 4 6 8 10 12 PRODUCTION RATE ('000 units/period) TOTAL ('000 $/period) \ Q 1 = 1000 (break even) Q 2 = 10 000 (profit limit) Using the quadratic equation: (-0.02) 2 000) (-200 (-0.02) 4 2 220 220 2 Q , 1 Q- - = 5...
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solutions to tutorial 4 - 1 McGill Faculty of Engineering...

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