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posted by  h8calqlas on 8/19/2009 7:30:44 PM  |  status: Closed  |  Earned Karma: 285

Differentiation 1

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Question Details:
A manufacturer's total monthly revenue is R(q) = 240q - .05q2 dollars when q units are produced during the month. Currently, the manufacturer is producing 80 units a month and is planning to decrease the monthly output by .65 unit. Estimate how the total monthly revenue will change as a result.

Please give simple steps so that I can understand.
Tags: Calculus
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posted by RedSox123 on 8/19/2009 7:39:53 PM  |  status: Live
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Response Details:
Since the change in output is small, we can approximate the change using the derivative.

dR/dq = 240 - .1q

Evaluating this at their current production level (80 units), we get dR/dq(80) = 232

Change in revenue = dR/dq * delta q = 232 * -.65 = -150.8
Oracle
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posted by anonymousxyz on 8/19/2009 7:46:13 PM  |  status: Live
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Response Details:
R(q)  =  240q  -  0.05q2

The total monthly revenue when 80 units are produced per month is:

R(80)  =  240(80)  -  0.05(80)2  =  18,880 dollars

The total monthly revenue when 80 - 0.65 = 79.35 units are produced per month is:

R(79.35)  =  240(79.35)  -  0.05(79.35)2  =  18,729.1789 dollars

The change in total monthly revenue when production decreases from 80 units per month to 79.35 units per month is:

18,729.1789 dollars  -  18,880 dollars  =  -150.8211 dollars

Final answer:

Total monthly revenue decreases by approximately 150.82 dollars when production decreases from 80 units per month to 79.35 units per month.
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