This is a simple probem
1 answer:
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The number of applicants is 20.
a).The number of ways 20 applicants can be split into two jobs is a question of combination as arrangment is not a necessity in this problem.
b).The number of ways in which 20 applicant can be split into these two jobs categories can be determined as,
Thus, there will be 21 ways in which the jobs can be split into these two categories.
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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