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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 167262 247.4 247.6 3025 167262.5 247.5 247.5 3030 167262 247.6 247.4 3035 167260.5 247.7 247.3 3040 167258 247.8 247.2 3045 167254.5 247.9 247.1 3050 167250 248 247 3055 167244.5 248.1 246.9 3060 167238 248.2 246.8 3065 167230.5 248.3 246.7 3070 167222 248.4 246.6 3075 167212.5 248.5 248.5 3080 167202 248.6 248.4 3085 167190.5 248.7 246.3 3090 167178 248.8 246.2 3095 167164.5 248.9
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