A Midwestern factory has been studying their costs and estimates thetotal cost for an upcoming production run can be modeled byC(x) = 41000 + 80x + x³ dollars. The total revenue from the sale ofx units is R(x) = 3680x dollars.Before they start production, they want to know if it will beworthwhile... That is, can they make money?(a) Find the profit function, (b) determine the level of production thatwill maximize profit, and (c) find the maximum profit possibleaccording to this model.a) The profit function is P(x)=Round the production level to the nearest whole unit.b) The production level per week that results in the maximum profit isUse the whole number you entered above to compute the maximumprofit.c) The maximum profit is $

Answered: A Midwestern factory has been studying…

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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Suppose a computer manufacturer has the total cost function C(x) = 80x + 3600 (in dollars) and the total revenue function R(x) (a) What is the equation of the profit function P(x) (in dollars) for this commodity? P(x) = (b) What is the profit (in dollars) on 348 items? P(348) = $ (c) How many items must be sold to avoid losing money? X = items = 380x (in dollars).
A contractor wants to rent a wood chipper from Acme Rental for a day for $143 plus $13 per hour or from Bell Rental for a day for $191 plus $9 per hour. Find a cost function in dollars for using each rental firm. (Let x be the number of hours for which the wood chipper is rented.) Acme C(x) = Bell C(x) = (a) Find the number of hours for which each cost function will give the same cost. hours(b) If the contractor wants to rent the wood chipper for 14 hours, which rental place will cost less? Acmecannot be determined Bellthey are the same
A supply company charges for 90-liter drums using the demand function p(x)=20.9−1.6x What is the revenue function?
4. It costs C(x) = 112 + 1.4x dollars to produce x Specialty Hair Ribbons. To sell x Specialty Hair Ribbons, the price should be set at p(x) = 18 - 0.2x. a.Find the revenue function R(x) and the profit function P(x) when the manufacturer makes and sells x ribbons. Simplify your functions. R(x) P(x) b. How many ribbons should be made and sold to break even? Round your answers) to the nearest whole number and include units. What profit (or loss) does the manufacture incur when they make and sell 32 ribbons? Circle profit or loss and fill in the blank below rounding to the nearest whole dollar. At a production level of 32 Ribbons, they have a profit / 1OSS of
Suppose demand is given by p = 1600 − x. Find the maximum revenue.
A. Find the average cost function for ? televisions produced. B. Find the instantaneous rate of change of the average cost function.
A small business's cost to produce I units of a new product is given by C(x) = -0.001x² + 4x+506 dollars. The business earns a revenue of R(x) 4x dollars from selling I units. Determine the marginal profit of the %D business at a production level of 306 units. Enter your answer to the nearest whole number.
Heller Manufacturing has two production facilities that manufacture baseball gloves. Production costs at the two facilities differ because of varying labor rates, local property taxes, type of equipment, capacity, and so on. The Dayton plant has weekly costs that can be expressed as a function of the number of gloves produced TCD(X) = X² X + 3 where X is the weekly production volume in thousands of units and TCD(X) is the cost in thousands of dollars. The Hamilton plant's weekly production costs are given by TCH(Y) y² + 2Y + 9 where Y is the weekly production volume in thousands of units and TCH(Y) is the cost in thousands of dollars. Heller Manufacturing would like to produce 5,000 gloves per week at the lowest possible cost. (a) Formulate a mathematical model that can be used to determine the optimal number of gloves to produce each week at each facility. min s.t. = X, Y Z 0 = 5 (b) Use Excel Solver or LINGO to find the solution to your mathematical model to determine the optimal…
A concert will be held at the end of April. Past experience indicates when tickets are priced at $70, the average attendance is 1400 people. Each $1 increase in price results in 14 fewer people attending. Let x represent the price of a concert ticket. (A) Determine a formula for the linear function, A(x), representing the quantity of tickets sold at a price x dollars. (B) Determine a simplified formula for the revenue function, (p A)(x), where p(x)=x is the price function and A(x) is the linear function from part (A). (C) Determine the maximum revenue ALGEBRAICALLY (no graphing). What should the venue charge for a ticket to maximize revenue? Include units with your answer.

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