MIME 310 - Tutorial Solutions 4

MIME 310 - Tutorial Solutions 4 - McGill Faculty of...

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1 McGill Faculty of Engineering MIME 310 Engineering Economy Tutorials Chapter 4. Production and Cost Analyses
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2 McGill Faculty of Engineering MIME 310 Engineering Economy Tutorials 4.1 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. 0 200 400 600 800 1000 1200 1400 02468 1 0 1 2 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 ± =
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3 McGill Faculty of Engineering MIME 310 Engineering Economy Tutorials ii) Maximum TP at MC=MR MC = dTC/dQ = 130 - 0.01 Q MR = dTR/dQ = 350 - 0.05 Q 130 - 0.01 Q = 350 - 0.05 Q 0.04 Q = 220 Q = 5500
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4 McGill Faculty of Engineering MIME 310 Engineering Economy Tutorials 4.2 The table below gives an incomplete account of the cost statistics associated with a particular production process. Determine the missing values. Production Rate (‘000 units/period) Total Costs (‘000 $ /period) Average Cost ($/unit) Incremental Cost ($/unit) 0 11 1 20 8 2 28 3 33 4 9 5 38 4 6 7 7 8 60 9 8 14 10
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5 McGill Faculty of Engineering MIME 310 Engineering Economy Tutorials 14 8 9 7 60 8 10 7 6 4 38 5 9 4 33 3 28 2 8 20 1 11 0 Incremental Cost ($/unit) Average Cost ($/unit) Total Costs (‘000 $/period) Production Rate (‘000 units/period) AC = TC / R TC = AC R TC 2 = TC 1 + IC R 20 - 11 = 9 38 + 4 = 42 42 + 7 = 49 72 + 14 = 86 20 / 1 = 20 28 / 2 = 14 33 / 3 = 11 38 / 5 = 7.6 60 / 8 = 7.5 60 - 49 = 11 33 - 28 = 5 36 - 33 = 3 38 - 36 = 2 72 - 60 = 12 Production Rate: R Total Costs: TC Average Cost: AC Incremental Cost: IC 9 (4) = 36 8 (9) = 72 42 / 6 = 7 49 / 7 = 7 86 / 10 = 8.6 TC 2 -TC 1 R IC =
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6 McGill
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This note was uploaded on 04/17/2010 for the course MIME 310 taught by Professor Bilido during the Fall '08 term at McGill.

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MIME 310 - Tutorial Solutions 4 - McGill Faculty of...

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