A fertilizer producer finds that it can sell its product at a price of p = 1500 – 0.3x dollars per unit when it produces x units of fertilizer. The total production cost (in dollars) for xunits is C(x) = 45,000 + 375x + 0.075x². If the production capacity of the firm is at most 1000 units of fertilizer in a specified time, how many units must be manufactured an sold in that time to maximize the profit? Selling units maximizes profit.

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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A fertilizer producer finds that it can sell its product at a price of p = 1500 – 0.3x dollars per unit when it produces x units of
fertilizer. The total production cost (in dollars) for xunits is
C(x) = 45,000 + 375x + 0.075x².
If the production capacity of the firm is at most 1000 units of fertilizer in a specified time, how many units must be manufactured and
sold in that time to maximize the profit?
Selling i
units maximizes profit.
Transcribed Image Text:A fertilizer producer finds that it can sell its product at a price of p = 1500 – 0.3x dollars per unit when it produces x units of fertilizer. The total production cost (in dollars) for xunits is C(x) = 45,000 + 375x + 0.075x². If the production capacity of the firm is at most 1000 units of fertilizer in a specified time, how many units must be manufactured and sold in that time to maximize the profit? Selling i units maximizes profit.
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