Question

Sally's anime club is selling brownies to raise money. Instead of just aiming blindly, Sally does some market research to try and maximize the club's profits. She develops the following model: \(P = -3P^2 + 8P + 145\) Where \(P\) is the amount the club will earn from the bake sale and \(P\) is the price they charge for each brownie, both measured in dollars. A: What price should the club charge for their brownies to maximize their profits? B: How much money should the club expect to make if they sell their brownies at this price?

          Sally's anime club is selling brownies to raise money. Instead of just aiming blindly, Sally does some market research to try and maximize the club's profits. She develops the following model:
\(P = -3P^2 + 8P + 145\)
Where \(P\) is the amount the club will earn from the bake sale and \(P\) is the price they charge for each brownie, both measured in dollars.
A: What price should the club charge for their brownies to maximize their profits?
B: How much money should the club expect to make if they sell their brownies at this price?

Sally's anime club is selling brownies to raise money. Instead of just aiming blindly, Sally does some market research to try and maximize the club's profits. She develops the following model:
P = -3P^2 + 8P + 145
Where P is the amount the club will earn from the bake sale and P is the price they charge for each brownie, both measured in dollars.
A: What price should the club charge for their brownies to maximize their profits?
B: How much money should the club expect to make if they sell their brownies at this price?

Added by Jason P.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Eduard Sanchez

07/04/2023

Step 1

Step 1: The model given is dθu/dx = p - x, where f(x) represents the profit earned from the bake sale and p is the price charged for each brownie. Show more…

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allyanimedu market research to try and maximize the ubx profit. She develops the following model: Where f(x) will earn from the bake sale and p is the price they charge for each brownie. dθu/dx = p - x She wants to find the value of x that maximizes the profit. To do this, she sets the derivative equal to zero: p - x = 0 Solving for x, she finds that x = p. Therefore, to maximize the profit, she should charge the same price for each brownie as the cost to make it.