5. A company has found that its weekly profit from the sale of x thousand hula hoops isgiven byP(x) = −0.02x³ + 600x − 20,000Production bottlenecks limit the number of hula hoops that can be made per week to nomore than 150, while a long-term contract requires that at least 50 hula hoops be madeeach week. Find the maximum possible weekly profit that the firm can make.

Answered: 5. A company has found that its weekly…

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 business includes a monthly promotion funding of $154000. The commerce division calculates that if x dollars are spent on an article advertisement and y dollars on a computer advertisement, then the monthly deals will have this equation provided: z = f(x, y) = 340x0.9 y^{0.9 Specify how much money the business should pay for article promotions and computer promotions monthly to make the best use of its monthly deals.
Suppose that for a company manufacturing calculators, the cost, revenue, and profit equations are given by x² 20' C = 90,000+ 40x, R=200x - where the production output in 1 week is x calculators. If production is increasing at a rate of 400 calculators per week when production output is 6,000 calculators. Find the rate of increase (decrease) in cost, revenue, and profit. A) Costs are increasing at the rate of $ (Simplify your answer.) B) Revenue is (Simplify your answer.) C) Profits are (Simplify your answer.) at the rate of $ P=R-C at the rate of $ per week at this production level. per week at this production level. per week at this production level.
A group of researchers found that people prefer YouTube videos that aren't too long, but not too short either. Suppose these researchers determined that the ratings people gave to a video could be approximated byR(t)=20t/t^2 + 100 where t is the length of the video in minutes and R(t) is its rating. What length of video (in minutes) will get the highest rating?
Suppose a firm’s profit function is given by π(q)=(1526*q-1*q^2 )-(1*q^2+11*q). What is the profit maximizing value of q?
A movie theater has a screen that is positioned 10 ft off the floor and is 25 ft high. The first row of seats is placed 9 ft from the screen and the rows are set 3 ft apart. The floor of the seating area is inclined at an angle of a = 20° above the horizontal and the distance up the incline that you sit is x. The theater has 21 rows of seats, so 0 < x< 60. Suppose you decide that the best place to sit is in the row where the angle 0 subtended by the screen at your eyes is a maximum. Let's also suppose that your eyes are 4 ft above the floor, as shown in the figure. 1. Show that a² + b2 – 625 arccos 2ab where a? = (9 + x cos a)² + (31 – x sin a)² and b? = (9 + x cos a)² + (x sin a – 6)² 2. Use a graph of 0 as a function of x to estimate the value of x that maximizes 0. In which row should you sit? What is the viewing angle 0 in this row?
Suppose the cost incurred in operating a cruise ship per hour is a+bv^33 dollars, where aand b are positive constants and v is the ship’s speed in miles per hour. At what speedshould the ship be operated between two ports (located d miles apart) to minimize thecost?
Suppose the function C(x) = 0.005x^3 − 0.15x^2 + 3x + 210 gives the daily cost to run a plastic tub factory on a day when x plastic tubs are manufactured.a) Find the marginal cost function. b) Find the marginal cost when 100 tubs have been manufactured. Explain this value in a sentence. c) Find the average cost per tub if 200 tubs are manufactured. d) Find the marginal average cost function C'(x).

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