a manufacturer charges $24 for headphones and has been selling 1000 of them per week. He estimated that for every $1 price reduction, 100 more headphones can be sold per week. What price should he charge for the headphones to maximize his total profit? Show your work.
1
Expert's answer
2012-01-27T08:48:04-0500
Assume x is price reduction. Let construct function of profit: 24 - x -price per one headphone,
also 1000+100x -number of sold headphones
then profit function looks like:
f = (24 - x) (1000 + 100x )
f = -100 x^2 + 1400x + 24000
we should find the value of x when this function has a maximum. For that take the first derivative:
f'= -200 x + 1400 in the point f'=0 we have maximum, so
Numbers and figures are an essential part of our world, necessary for almost everything we do every day. As important…
APPROVED BY CLIENTS
"assignmentexpert.com" is professional group of people in Math subjects! They did assignments in very high level of mathematical modelling in the best quality. Thanks a lot
Comments
Leave a comment