SOLUTION: Mrs. Inere can sell 50 brownie boxes each month if she charges $95 for each box. She estimates that for every $5 increase in price, she will sell 2 boxes less. Find the price that

Question 1125542: Mrs. Inere can sell 50 brownie boxes each month if she charges $95 for each box. She estimates that for every $5 increase in price, she will sell 2 boxes less. Find the price that would yield the maximum revenue.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
she sells 50 brownie boxes when they are 95 dollars each.

her total revenue is 50 * 95 = 4750

she estimates that she will sell 2 boxes less for every 5 dollar incfrease in the price of 1 box.

the equation for that is y = (50 - 2x) * (95 + 5x).

each time x goes up 1 unit, the number of boxes goes down 2 and the price of each box goes up 5.

multiply the factors together to get y = 50 * 95 + 50 * 5x - 2x * 95 - 2x * 5x.

simplify to get y = 4750 + 250x - 190x - 10x^2

combine like terms to get y = 4750 + 60x - 10x^2

rearrange the terms in descending order of degree to get:

y - -10x^2 + 60x + 4750

this is a quadratic equation in standard form where:

a = -10
b = 60
c = 4750

the maximum value of this equation will occur when x = -b/(2a)

x = -b/(2a) becomes x = -60 / -20 = 3.

when x = 3, y = -10 * 3^2 + 60 * 3 + 4750 = 4840.

when x = 3, she sells 50 - 6 = 44 boxes at 95 + 15 = 110 dollars each for total revenue of 44 * 110 = 4840.

for her, it doesn't get any better than that.

here's the graph of the equation that shows when the maximum revenue occurs.

$$$

the blue line is the graph of the equations.

since the equations are equivalent, they draw the same line on the graph.

the orange line is there to show the value of the curve when x = 3.

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