Respuesta :
The equation of profit will be P = -600p² + 28,000p - 250,000. Then the maximum profit is $ 76,667 at a maximum profit price $ 23.33.
What is a profit?
A monetary profit, particularly the distinction between the amount gained and the actual cost of purchasing, running or creating anything.
The expense function for a widget is E = -3,000p + 250,000.
The revenue function is R = -600p² + 25,000p.
Then the profit equation is in simplified form (P = R- E).
P = (-600p² + 25,000p) - (-3,000p + 250,000)
P = -600p² + 25,000p + 3,000p - 250,000
P = -600p² + 28,000p - 250,000
Then the maximum profit will be
Differentiate P with respect to p, then we have
P' = -1,200p + 28,000
For maximum profit P" < 0, P' = 0. Then we have
P" = -1,200
P" < 0
Then we have
P' = 0
-1,200p + 28,000 = 0
1,200p = 28,000
p = 23.33
Then the profit will be
P = -600(23.33)² + 28,000(23.33) - 250,000
P = -326,573.34 + 653,240 - 250,000
P = 76,666.67
P ≅ 76,667
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