Question 996730: In the planning of a taco restaurant, we estimate that if there is seating for between 10 and 40 people, the daily profit will be $10 per seat. However, if the seating capacity is more than 40 places, the daily profit per seat will be decreased by $0.20 per seat. What should the seating capacity be in order to maximize the taco restaurant’s total profit?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In the planning of a taco restaurant, we estimate that if there is seating for between 10 and 40 people, the daily profit will be $10 per seat. However, if the seating capacity is more than 40 places, the daily profit per seat will be decreased by $0.20 per seat. What should the seating capacity be in order to maximize the taco restaurant’s total profit?
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Profit = (# of seats)(profit per seat)
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Equation to Maximize::
P(x) = (40+x)(10-0.20x)
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P(x) = 400 +10x-8x - 0.2x^2
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Find the derivative and solve for zero::
-0.4x +2 = 0
x = 5
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Ans: Seating capacity should be 45
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Cheers,
Stan H.
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