Question

Set up a revenue function, R(n), that can be used to solve the problem, then solve the problem. A business sells n exploding cigars, n ≤ 25, at a price of (25 - 0.2n) dollars per cigar. How many exploding cigars must be sold to have a revenue of $120?

Answer 1

• R(n) = n·(25 -0.2n)

• n = 5

Explanation:

Revenue is the product of selling price and the number sold. If n cigars are sold at a price of (25-0.2n), then the revenue generated is ...

R(n) = n(25 -0.2n)

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We want the value of this to be 120, so we want the solution to ...

120 = n(25 -0.2n)

0.2n^2 -25n +120 = 0

n^2 -125n +600 = 0

(n-5)(n-120) = 0

n = 5 . . . . . . . any value above 25 is extraneous

The revenue function is R(n) = n(25-0.2n); 5 cigars must be sold to have a revenue of $120.