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A company manufacturers and sells x electric drills per month. The monthly cost and price-demand equations are

C(x)=64000+60x, p=190−x/30, 0≤x≤5000.

Aproduction level at max revenue = 2850
Bprice to max profit = $125
CSuppose that a 5 dollar per drill tax is imposed. Determine the number of drills that should be produced and sold in order to maximize profit under these new circumstances. ???

Verified Answer :

jessican2017

A.
Revenue x p = 220x - x^2/30

d/dx = 220 15 = 3300

B.
Profit = Revenue - Cost

= 220x - x^2/30 - 72000 - 80x

d/dx = 220 - x/15 - 80 = 0

x = 15 140 = 2100

p = 220 - 2100/30 = 220 - 70 = $150

C.
With $5 tax the price-demand equation should be

p = 220 - x/30 + 5

Profit = 225x - x^2/30 - 72000 - 80x

d/dx = 225 - x/15 - 80 = 0

x = 15 145 = 2175

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