Calc
posted by dylan on .
a fast food place sells 425 large orders of fries per week at price $2.75 each. A market survey indicates that for each $0.10 decrease, sales will increase by 20 orders of fires
a) Determine the ,marginal revenue function
b) With what price with marginal revenue be equal to zero, interpret this value

let the number of 10 cent decreases by n
then price of fries = 2.75.1n
number sold = 425 + 20n
revenue = (2.75.1n)(425+20n)
d(revenue)/dx = (2.75.1)(20) + (425+20n)(.1) = 0 for a max of revenue
55  2n  42.5  2n = 0
4n = 12.5
n = 3.125
I would assume that the decreases would be complete multiples of 10 cents, so there should be 3 decreases or a 30 cent decrease
when n = 3
they will have a price of 2.45
and they will sell 485
revenue = 2.45(485) = 1188.25
check:
if n=2
revenue = 2.55(465) = 1185.75 , which is lower
if n=4
revenue = 2.35(505 = 1186.75 , which is also lower than the n=3 value