The expense function for a widget is E = -3,000p + 250,000. The revenue function is R = -600p^2 + 25,000p. Write the profit equation in simplified form ( P= R- E) . Use the axis of symmetry formula to determine the maximum profit price and the maximum profit.

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abidemiokin abidemiokin · Answer 1 · 2022-06-15T19:17:12+02:00

The maximum profit price and maximum profit are 23.33 and 301666.66 respectively

Given the following functions

Expense = E = -3,000p + 250,000.

The revenue function is R = -600p^2 + 25,000p

The profit is the difference between the revenue and cost to have;

P = R - E

P = -600p^2 + 25,000p - ( -3,000p + 250,000.)

Simplify

P = -600p^2 + 25,000p - ( -3,000p + 250,000.)

P = -600p^2 + 25,000p +3,000p- 250,000

P = -600p^2 + 28000p - 250000

The maximum price occurs when P'(p) = 0

P'(p) = -1200p + 28000

0 = -1200p + 28000

p = 28000/1200
p = 23.33

Substitute

P(23.33) = -600(23.33)^2 + 28000(23.33) - 250000

P(23.33) = -326573.34 - 250000 + 653240

P(23.33) = 301666.66

Hence the maximum profit price and maximum profit are 23.33 and 301666.66 respectively

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