The Jones family is considering which one of two businesses will mow their
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182.5 is the maximum revenue.
What do revenue means?
- Revenue is the total amount of income generated by the sale of goods or services related to the company's primary operations.
- Revenue, also known as gross sales, is often referred to as the "top line" because it sits at the top of the income statement.
- Income, or net income, is a company's total earnings or profit.
Revenue = p(x) × x = ( 300 - x /30)x
⇒R(x) = 300x - x²/30
R'(x) =
300 - x /15 = 0
⇒ x = 300 . 15 = 4500
∴ Max Revenue = R(4500) = 300 . 4500 - 4500²/30 = 675000 $
Profit = Revenue - cost
P(x) = 300x - x²/30 - (75000 + 60x)
P'(x) = d/dx ( 300x - x²/30 - ( 75000 + 60x)
= d/dx (300x) - d/dx (x²/30) - d/dx ( 75000 + 60z))
= 300 - x /15 -60
= 240 - x /15
P'(x) = 0 ⇒ x = 240 . 15 = 3600
P(3600) = 300 .3600 - 3600²/30 - (75000 +60 . 3600) =357000
∴ Max profit is 357000$ when 3600 sets are manufactured
After taxation , p(x) = 300x - x²/30 - ( 75000 + 60x) -5x
P'(x) = 300x - x²/30 - ( 75000 + 60x) -5x
= d/dx (300x) - d/dx (x²/30) - d/dx ( 75000 + 60x ) - d/dx (5x)
= 300 - x/15 - 60 -5 = 235 - x/15
P'(x) = 0 ⇒ x = 235 . 15 = 3525
Pmax = P(3525) = 300 .3525 - 3525²/30 - ( 75000 + 60 .3525) - 5 .3525= 678375/2 (Decimal ; 339187.5)
P(3525) = 300 - 3525/30 = 365/2 = 182.5
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