You want to sell a certain number n of items in order to maximize your profit. Market research tells you that if you set the price at $1.50, you will be able to sell 5000 items, and for every 10 cents you lower the price below $1.50 you will be able to sell another 1000 items. Suppose that your fixed costs ("start-up costs'') total $2000, and the per item cost of production ("marginal cost'') is $0.50. Find the price to set per item and the number of items sold in order to maximize profit, and also determine the maximum profit you can get

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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You want to sell a certain number n of items in order to maximize your profit. Market research tells you that if you set the price at $1.50, you will be able to sell 5000 items, and for every 10 cents you lower the price below $1.50 you will be able to sell another 1000 items. Suppose that your fixed costs ("start-up costs'') total $2000, and the per item cost of production ("marginal cost'') is $0.50. Find the price to set per item and the number of items sold in order to maximize profit, and also determine the maximum profit you can get.

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