Answer to Question #343191 in Calculus for CHUA

Question #343191

A company manufactures and sells x televisions per month. If the cost and the

revenue functions (in dollars) are


C(x) = 72, 000 + 60x and R(x) = 200x − X2 / 30


respectively, with 0 ≤ x ≤ 6, 000, what will the approximate changes in revenue and

profit be if the production is increased from 1, 500 to 1, 505? from 4, 500 to 4, 505?


1
Expert's answer
2022-05-22T23:16:34-0400

R(1500)=200x1500-(1500)2/30=300000-75000=225000

R(1505)=200x1505-(1505)2/30=300000-75000=225499

Revenue becomes greater by 225499-225000=499 $ or by 225499x100/225000-100=0.22%

P(x)=R(x)-C(x)=200x-x2/30-72000-60x=140x-x2/30-72000

P(1500)=140x1500-(15002)/30-72000=63000

P(1505)=140x1505-(15052)/30-72000=63199

Profit becomes greater by 63199-63000=199$ or by 63199x100/63000-100=0.32%


R(4500)=200x4500-(4500)2/30=225000


R(4505)=200x4505-(4505)2/30=224499


Revenue becomes smaller by 225000-224499=499 $ or by 225000x100/224499-100=0.22%


P(4500)=140x4500-(45002)/30-72000=-117000


P(4505)=140x4505-(45052)/30-72000=-117801


Profit becomes smaller by -117000-(-117801)=801$ or by -117801x100/-117000-100=0.68%



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