3. You may use your graphing calculator for this problem. Make sure to explain your answers, including what you did to find each answer. A pharmaceutical company can calculate their monthly profit for selling its signature drug, using the function below, where x represents the number of pounds of the product they sell, and p(x) is measured in hundreds of dollars. p(x) = 3.5x? + 24x – 0.1x3 150 %3D a. How many pounds of the drug must they sell to maximize their monthly profit? How much money would that net for the company? Justify your answer. b. If the company sells 17 pounds of their medication, would their monthly profit be increasing or decreasing? Justify your answer. c. If the company sells 5 pounds of their drug, their profit will be $4500. If they sell 15 pounds, their profit will be $66,000. Explain why there must be an amount of pounds, x, between 5 and 15 pounds, where the rate of the profit would be increasing by $6150 per pound.
3. You may use your graphing calculator for this problem. Make sure to explain your answers, including what you did to find each answer. A pharmaceutical company can calculate their monthly profit for selling its signature drug, using the function below, where x represents the number of pounds of the product they sell, and p(x) is measured in hundreds of dollars. p(x) = 3.5x? + 24x – 0.1x3 150 %3D a. How many pounds of the drug must they sell to maximize their monthly profit? How much money would that net for the company? Justify your answer. b. If the company sells 17 pounds of their medication, would their monthly profit be increasing or decreasing? Justify your answer. c. If the company sells 5 pounds of their drug, their profit will be $4500. If they sell 15 pounds, their profit will be $66,000. Explain why there must be an amount of pounds, x, between 5 and 15 pounds, where the rate of the profit would be increasing by $6150 per pound.
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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Transcribed Image Text:3. You may use your graphing calculator for this problem. Make sure to
explain your answers, including what you did to find each answer.
A pharmaceutical company can calculate their monthly profit for selling its
signature drug, using the function below, where x represents the number of
pounds of the product they sell, and p(x) is measured in hundreds of
dollars.
p(x) = 3.5x² + 24x – 0.1x³ – 150
a. How many pounds of the drug must they sell to maximize their monthly
profit? How much money would that net for the company? Justify your
answer.
b. If the company sells 17 pounds of their medication, would their monthly
profit be increasing or decreasing? Justify your answer.
c. If the company sells 5 pounds of their drug, their profit will be $4500. If
they sell 15 pounds, their profit will be $66,000. Explain why there must
be an amount of pounds, x, between 5 and 15 pounds, where the rate of
the profit would be increasing by $6150 per pound.
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