SOLUTION: assume that i sell 66 sandwiches when selling them for $1. if i lose 5 customers each time i raise the price $.25, what is the price that will produce the higherst amount of sales?

Question 308886: assume that i sell 66 sandwiches when selling them for $1. if i lose 5 customers each time i raise the price $.25, what is the price that will produce the higherst amount of sales? what is the amount of money i will bring in? solve using quadratics.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
assume that i sell 66 sandwiches when selling them for $1. if i lose 5 customers each time i raise the price $.25, what is the price that will
produce the highest amount of sales?
what is the amount of money i will bring in? solve using quadratics.
:
Let x = no. of .25 increases & no. of 5 customer decreases
:
Revenue = price * no. sold
R(x) = (1 + .25x)(66 - 5x)
FOIL
R(x) = 66 - 5x + 16.5x - 1.25x^2
R(x) = 66 + 11.5x - 1.25x^2
A quadratic equation
y = -1.25x^2 + 11.5x + 66
Find the axis of symmetry; x = -b/(2a), a=-1.25, b=+11.5
x =
x =
x = 4.6 ~ 5, have to have an integer
Price for max revenue: 1 + 5(.25) = $2.25
No. sold: 66 - 5(5) = 41 sold
:
Find the max revenue; substitute 5 for x in the quadratic equation
R(x) = -1.25(5^2) + 11.5(5) + 66
R(x) = -1.25(25) + 57.5 + 66
R(x) = -32.25 + 57.5 + 66
R(x) = $92.25
:
Check: Price * no. sold
2.25 * 41 = 92.25 max sales

RELATED QUESTIONS
assume that you sell 65 sandwiches for $1 each. if you lose 8 customers each time you... (answered by ankor@dixie-net.com)

You sell widgets for $10 and have 500 customers. For every .25 cents you raise the price... (answered by stanbon)

The problem is: A DVD company wants to maximize its revenue. the company now sells dvd's (answered by Paul)

1. You sell peanuts at UNK athletic events to make some extra money. When peanuts are... (answered by CPhill)

I needhelp setting up this word problem. You have to sell 50 tickets to a fair. Student... (answered by stanbon)

I have tried and tried to remember the formulas and have done research to refresh my... (answered by cristiana)

Vinnie owns a t-shirt shop. He has determined that he can sell 150 t-shirts for $10 each. (answered by josmiceli)

I am helping my daughter (8th grade) with math and the word problems are as frustrating... (answered by Alan3354)

Pauline wants to sell stainless steel water bottles as a school fundraiser. She knows... (answered by ankor@dixie-net.com)