SOLUTION: The cost c(x) in dollars of producing x calculators is given c(x)=16000+120x and the revenue R(x) is R(x)=700x-x^2/50. Find the profit P(x), where P(x)=R(x)-C(x), when 500 calcula

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The cost c(x) in dollars of producing x calculators is given c(x)=16000+120x and the revenue R(x) is R(x)=700x-x^2/50. Find the profit P(x), where P(x)=R(x)-C(x), when 500 calcula      Log On


   

Question 61666: The cost c(x) in dollars of producing x calculators is given c(x)=16000+120x and the revenue R(x) is R(x)=700x-x^2/50. Find the profit P(x), where P(x)=R(x)-C(x), when 500 calculators are produced and sold.
Answer by 303795(602) About Me  (Show Source):
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The cost of producing 500 calculators is given by the cost formula
c(x)=16000+120x Substitute x = 500 into this formula.
Cost = 16000 + 120 * 500
= $76 000

The revenue gained from selling the 500 calculators is given by
R(x)=700x-x^2/50. Substitute x = 500 into this formula.
Revenue = 700*500 - 500^2/50
=$345 000

The profit formula is P(x)=R(x)-C(x)
Profit = $345 000 - $76 000
=$269 000

(Note that if only a few calculators were produced then the cost function would be larger than the revenue function and the profit would be negative. This would mean that a loss had been made.)