The cost of producing x vials of COVID-19 vaccine is given byx2C(x) = 300000 + 5000x +2A chemical manufacturer decides to commercialize the vaccine and finds that the price demand equationis given byp(x) = 70002Find the maximum profit that can be received from selling the vaccines.

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Answered: The cost of producing x vials of…

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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D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item, and S(x) is the price, in dollars per unit, that producers are willing to accept for x units. If the equilibrium price is $12 and the equilibrium quantity is 144 units, find the Consumer Surplus at the equilibrium point and then answer the question about Producer Surplus. 144 D(x)= S(x) = Vx %3D You must write a complete solution for part (a) and submit with your written work. Note: Consumer and Producer Surplus formulas are: Consumer Surplus: D(x)dx- PQ, Producer Surplus: PQ- | Sx)dx. [4 points] (a) The Consumer Surplus is S (Round to the nearest cent as needed.) (b) Which expression will give the correct value of the Producer Surplus? [2 points] O A. T 1 1A-(12|144) 0. -144 -(12)(144) |O B. 21 (12)(144)- [144 -0 OC. 3 2. 2, 21 144 3. (12)(144) D. 31 (12)(144)- 2. 144 E. (12)(144)- [12 -0 (Select the correct answer.) Click to select your answer(s).
Suppose demand is given by p = 1600 − x. Find the maximum revenue.
Suppose a company has fixed costs of $32,000 and variable cost per unit of 1/3x + 444 dollars,where x is the total number of units produced. Suppose further that the selling price of its product is 1,476 −2/3x dollars per unit. (a) Form the cost function and revenue function (in dollars). C(x)=? R(x)=? Find the break-even points. x=? (b) Find the vertex of the revenue function. (x, y) =? Identify the maximum revenue. $_____=? (c) Form the profit function from the cost and revenue functions (in dollars). P(x)=? Find the vertex of the profit function. (x,y)=? Identify the maximum profit. $___=? (d)=What price will maximize the profit? $____=?
Suppose that the cost function C for a chemical lab to produce x liters sanitizer liquid per week is given by C(x)=5000+ Vx-0.001x°(RM). The lab set the price pand amount x liters sold follow the demand equation p(x)= 60–0.0005x° (RM). As an intern in the lab, you are required to find the break-even point, that is, how much it should produce the liquid per week in order to have neither a profit nor a loss. Use the Secant method with error tolerance 5x10² to approximate the break-even point. Begin your search with po-50 and pi=200. Show all the necessary working steps and write your answer in 4 decimal places.
Suppose that the demand equation and the cost function are given by –p = 125 − 0.1q C(q) = 800 + 12q + 0.02q2 Find the quantity q that maximizes the profit. What is the maximumprofit?

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The cost of producing x vials of COVID-19 vaccine is given by x2 C(x) = 300000 + 5000x + 2 A chemical manufacturer decides to commercialize the vaccine and finds that the price demand equation is given by p(x) = 7000 2 Find the maximum profit that can be received from selling the vaccines.