A company produces and sells chili powder. The company's weekly profit on the sale of x kilograms of chili powder is modeled by the function P given by P(x) = 48x + 1.4*x2-0.05*x2.8-270, where P(x) is in dollars and 0 ≦x≦80.(a) Find the rate, in dollars per kilogram, at which the company's weekly profit is changing when it sells 32 kilograms of chili powder. Is the company's weekly profit increasing or decreasing when it sells 32 kilograms of chili powder? Give a reason for your answer.b) How many kilograms of chili powder must the company sell to maximize its weekly profit? Justify your answer.c) The company plans to have a one-day sale on chili powder. Management estimates that t hours after the company store opens, chili powder will sell at a rate modeled by the function S given byS(t) =2 +cos（π/10t2) kilograms per hour. Based on this model, estimate the amount of chili powder, in kilograms, that will be sold during the first 5 hours of the sale(d) Using the function S from part (c), find the value of S'(3). Interpret the meaning of this value in the context of the problem Show your work and/or reasoning to receive credit.1.A company produces and sells chili powder. The company's weekly profit on the sale of x kilograms of chilipowder is modeled by the function P given by P(x) = 48x + 1.4x² – 0.05.x².8 – 270, where P(x) is in dollarsand 0 < x < 80.(a) Find the rate, in dollars per kilogram, at which the company's weekly profit is changing when it sells32 kilograms of chili powder. Is the company’s weekly profit increasing or decreasing when it sells32 kilograms of chili powder? Give a reason for your answer.(b) How many kilograms of chili powder must the company sell to maximize its weekly profit? Justify youranswer.(c) The company plans to have a one-day sale on chili powder. Management estimates that t hours after thecompany store opens, chili powder will sell at a rate modeled by the function S given byS(t) = 2 + cos10kilograms per hour. Based on this model, estimate the amount of chili powder, inkilograms, that will be sold during the first 5 hours of the sale.(d) Using the function S from part (c), find the value of S'(3). Interpret the meaning of this value in thecontext of the problem.

(a) Here, we have weekly profit P(x)=48x+1.4x2-0.05x2.8-270. So, the rate of change is…

Answered: A company produces and sells chili…

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 company produces and sells chili powder. The company's weekly profit on the sale of x kilograms of chili powder is modeled by the function P given by P(x) = 48x + 1.4*x²-0.05*x^2.8-270, where P(x) is in dollars and 0 ≦x≦80.

(a) Find the rate, in dollars per kilogram, at which the company's weekly profit is changing when it sells 32 kilograms of chili powder. Is the company's weekly profit increasing or decreasing when it sells 32 kilograms of chili powder? Give a reason for your answer.

b) How many kilograms of chili powder must the company sell to maximize its weekly profit? Justify your answer.

c) The company plans to have a one-day sale on chili powder. Management estimates that t hours after the company store opens, chili powder will sell at a rate modeled by the function S given by

S(t) =2 +cos（π/10t²) kilograms per hour. Based on this model, estimate the amount of chili powder, in kilograms, that will be sold during the first 5 hours of the sale

(d) Using the function S from part (c), find the value of S'(3). Interpret the meaning of this value in the context of the problem

Show your work and/or reasoning to receive credit.
1.
A company produces and sells chili powder. The company's weekly profit on the sale of x kilograms of chili
powder is modeled by the function P given by P(x) = 48x + 1.4x² – 0.05.x².8 – 270, where P(x) is in dollars
and 0 < x < 80.
(a) Find the rate, in dollars per kilogram, at which the company's weekly profit is changing when it sells
32 kilograms of chili powder. Is the company’s weekly profit increasing or decreasing when it sells
32 kilograms of chili powder? Give a reason for your answer.
(b) How many kilograms of chili powder must the company sell to maximize its weekly profit? Justify your
answer.
(c) The company plans to have a one-day sale on chili powder. Management estimates that t hours after the
company store opens, chili powder will sell at a rate modeled by the function S given by
S(t) = 2 + cos
10
kilograms per hour. Based on this model, estimate the amount of chili powder, in
kilograms, that will be sold during the first 5 hours of the sale.
(d) Using the function S from part (c), find the value of S'(3). Interpret the meaning of this value in the
context of the problem.

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