MarcKrishkeMath1600Project9

MarcKrishkeMath1600Project9 - Proj ects Chapter 9: Limits...

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P r o j e c t s Chapter 9: Limits and The Derivative Function
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Source: " Mathematical Applications" sixth edition by Harshbarger/Reynolds 1. (a) C(x) = 3x + 6000 R(x) = 12x – 0.001x 2 C'(x) = 3 R'(x) = 12 – 0.001(2)x = 12 – 0.002x The profit is P(x) = R(x) – C(x) = 12x – 0.001x 2 – 3x – 6000 = – 0.001x 2 + 9x – 6000 x Profit –0.001x 2 + 9x – 6000 3 = MC x MR 002 . 0 12 - = 4000 14000 3 4 4100 14090 3 3.8 4200 14160 3 3.6 4300 14210 3 3.4 4400 14240 3 3.2 4500 14250 3 3 4600 14240 3 2.8
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4700 14210 3 2.6 4800 14160 3 2.4 4900 14090 3 2.2 5000 14000 3 2.0 (b) C(x) = 187x + 0.01x 2 + 15750 R(x) = 308x – 0.01x 2 C'(x) = 187 + 0.01(2)x = 187 + 0.02x R'(x) = 308 – 0.01(2)x = 308 – 0.02x The profit is P(x) = R(x) – C(x) = 308x – 0.01x 2 – 187x – 0.01x 2 – 15750 = –0.01x 2 + 121x – 15750 x Profit –0.01x 2 + 121x – 15750 x MC 02 . 0 187 + = x x MR 02 . 0 308 - = 3000 167250 247 248 3005 167254.5 247.1 247.9 3010 167258 247.2 247.8 3015 167260.5 247.3 247.7 3020
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This note was uploaded on 03/16/2011 for the course MATH 1600 taught by Professor Calc during the Spring '11 term at Macomb Community College.

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MarcKrishkeMath1600Project9 - Proj ects Chapter 9: Limits...

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