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2 years ago

HELP PLEASE?? picture included to understand the question

Mathematics

1 answer:

aleksklad [387]2 years ago

6 0

Answer:

$77, 456

Step-by-step explanation:

Let P(x) = profit

P(x) = revenue - cost

⇒ P(x) = (952x - 0.68x²) - (-153x + 371450)

⇒ P(x) = -0.68x² + 1105x - 371450

Differentiate P(x)

⇒ P'(x) = -1.36x + 1105

Set P'(x) = 0 and solve for x:

⇒ -1.36x + 1105 = 0

⇒ 1.36x = 1105

⇒ x = 812.5

Therefore, maximum profit when x = 812.5

Substitute x = 812.5 into P(x):

P(812.5) = -0.68(812.5)²+ 1105(812.5) - 371450 = 77456.25

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