2. In a manufacturing plant, the cost of producing each unit of a product is modeled by the function C(x) = 2x² +100x + 10, where x is the number of units produced. The revenue generated from selling each unit is modeled bythe function R(x) = 20x-5.Find and interpret the expression for the profit function (P(x)) as a combination of these two functions, anddetermine the production level at which the company maximizes its profit. [✔✔✔✔]

The given cost function and the revenue function .The aim is to find the profit function and the…

Answered: In a manufacturing plant, the cost of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A firm sells a product for $80 per unit. Raw material costs are$12,50 per unit, labor costs are $27,50 per unit, and annual fixedcosts are $260,000.a. Determine the profit function P(x), where x equals the numberof units sold.b. How many units would have to be sold to earn an annualprofit of $250,000.
A company manufactures and sells x cell phones per week. The weekly price demand and cost functions are given respectively p(x) = 600 – 0.5x and C(x) = 20,000 + 130x. The maximum weekly profit is: A. $170,000. B. $81,100. C. $100,000. D. $90,450. Select one: O A O B O D
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 dairy spends $24,000 per year to maintain its barns and equipment. It costs $2000 per year to feed and care for each dairy cow. (a) Using C for the number of dairy cows and E for the total yearly expense, in dollars, find a formula that gives the total yearly expense as a linear function of the number of dairy cows. E = (b) Use functional notation to express the total expense if the dairy has 40 cows. E(40) E(40C) 40E E(2000) E(24,000) (c) Calculate the value from part (b). $
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A small bicycle manufacturer has daily fixed costs of $1958 and each bicycle costs $78 to manufacture. Let x represent the number of bicycles manufactured and C(x) represents the cost of manufacturing. Complete parts (a) through (c). www. (a) Write a linear function that models this situation. C(x) = (b) Find C(6). Interpret your answer in the context of this problem. C(6)=. This means that the cost of manufacturing bicycles in a day is $ A (c) Find the value of x if C(x) = 2738. Express this situation using function notation, and interpret it in the context of this problem. when C(x) = 2738. This means that the cost of manufacturing bicycles in a day is $
Find the maximum profit

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