Question

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

Answer 1

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