Answer to Question #343201 in Calculus for CHUA

Question

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?

Answer 1

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

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

Revenue become 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%