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 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

Q: Find the equation of the function g(x) described above.

A: We know that if the graph of function y=f(x) is stretched by a units(a>0, shifted to the right by…

Q: The ideal weight w (in pounds) of a man is a function of his height h (in inches). This function is…

A:

Q: The amount of foreign earnings (in trillions of dollars) kept overseas can be approximated by the…

A:

Q: Given a revenue function R(x)=1,000+x2−e2x, calculate the average revenue when x=3. Give your…

A: Given: Revenue function given by: R(x) = 1000 + x2 - e2x To Find: Average Revenue when x = 3 Formula…

Q: Find the number of pounds of salt in the tank as a function of time.

A:

Q: Starting with the graph of f(x) = 2, write the equation of the graph that results from (a) shifting…

A: Given graph equation , f(x)=2x (a) shifting f(x) 1 units upward, y= f(x)+1 =2x+1. (b) shifting f(x)…

Q: Find the domain of the function : h(x) =4/[(3/x) - 1]

A: Find the domain of the function : h(x) =4/[(3/x) - 1]

Q: The function f(x) = 4(2)x models the length of an image in centimeters after it has been enlarged by…

A:

Q: The amount of foreign earnings (in trillions of dollars) kept overseas can be approximated by the…

A: Given, The amount of foreign earnings kept overseas can be approximated by the function f(x) =…

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.