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 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 = {{{(-11.5)/(2*-1.25)}}} 
x = {{{(-11.5)/(-2.5)}}}
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