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.

a) production level at max revenue = 2850

b) price to max profit = $125

c) Suppose 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.?

Question

Mathematics

Paris Middleton

27 August, 08:07

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.

a) production level at max revenue = 2850

b) price to max profit = $125

c) Suppose 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.?

+1

Answers (1)

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Jadiel Reeves · Answer 1

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