Question

Ashwin charges $18 for a custom made t-shirt. He normally sells 350 t-shirts a month. After surveying customers Ashwin discovers that for every $0.50 price reduction he sells an additional 15 shirts. Write a let statement for the independent variable you would use to model this relation (where Revenue is the dependant variable) and thenFor the question above write the equation you would use to model this relation. *

Answer 1

let the number of $.5 price reductions be n

right now:
cost of shirt = 18
number sold = 350

after reduction:
cost of each shirt = 18 - .5n = .5(36 - n)
number sold = 350 + 15n = 5(70 + 3n)

Revenue = .5(36 - n)*5(70 + 3n)
= 2.5(2520 + 38n - 3n^2)

d(Revenue)/dn = 2.5(38 - 6n) = 0 for a max of Revenue
38 - 6n = 0
n = 19/3 reductions of $0.50

guess I could have stopped after finding Revenue.