SOLUTION: Carlos owns a vending machine in a bowling alley. He currently sells 600 cans of soda per week at $1.25 per can. He estimates that he will lose 40 customers for every increase in t

Question 389446: Carlos owns a vending machine in a bowling alley. He currently sells 600 cans of soda per week at $1.25 per can. He estimates that he will lose 40 customers for every increase in the price and gain 40 customers for every $0.05 decrease in the price.
1. Write a quadratic equation for the price increase
2. If Carlos lowers the price, what price should he charge in order to maximize his income?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Carlos owns a vending machine in a bowling alley.
He currently sells 600 cans of soda per week at $1.25 per can.
He estimates that he will lose 40 customers for every increase in the price
and gain 40 customers for every $0.05 decrease in the price.
:
1. Write a quadratic equation for the price increase
Let x = no. of .05 increases
Let x = no. of 40 customer decreases
:
f(x) = (1.25 + .05x)*(600 - 40x)
FOIL
f(x) = 750 - 50x + 30x - 2x^2
f(x) = -2x^2 - 20x + 750
:
2. If Carlos lowers the price, what price should he charge in order to maximize his income?
Just change the signs of the above equation
f(x) = (1.25 - .05x)*(600 + 40x)
f(x) = 750 + 50x - 30x - 2x^2
f(x) = -2x^2 + 20x + 750
cost for max income will be at the axis of symmetry; x = -b/(2a)
x = -2; b=20
x =
x = +5 ea .05 decreases in price, give 5(40) = 200 can increase
:
A .25 decrease; he should charge $1.00 for each soda, and will sell 800 cans
a total: $800, which is $50 more than selling it at $1.25 (1.25*600=$750)

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