(F) Graph the cost function and the revenue function on thesame coordinate system for 0 46. Revenue, cost, and profit. The price-demand equation andthe cost function for the production of HDTVS are given,respectively, byx = 9,000 – 30pandC(x) = 150,000 + 30xwhere x is the number of HDTVS that can be sold at a priceof $p per TV and C(x) is the total cost (in dollars) of produc-ing x TVs.

Answered: Image /qna-images/answer/c537d095-64d1-4fce-8eea-6e24e611be58.jpg

Answered: 46. Revenue, cost, and profit. The…

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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Similar questions

If the demand function for a product is given by p(x) = -0.25x² + x + 99 , where x is the number of units demanded and p is the price per unit in $. Then The revenue of selling 6 units is %3D
A. Find the average cost function for ? televisions produced. B. Find the instantaneous rate of change of the average cost function.
(a) A company has determined that its profit for a product can be described by a linear function. The profit from the production and sale of 150 units is $455, and the profit from 250 units is $895. (i) What is the average rate of change of the profit for this product when between 150 and 250 units are sold? (ii) Write the equation of the profit function for this product. (iii) How many units give break-even for this product? (b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p = 40 − 4q 2 where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass (i) Write an equation giving profit as a function of the number of lightweight compasses produced. (ii) At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the…
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). $
The manufacturing laundry sinks has fixed costs if $100 per day but has total costs of $2,500 per day when producing 15 sinks. The company has a daily demand function of q =360 – p, where q is the number of laundry sinks demanded and p is the price of a laundry sink. 1. If we assume that the total cost per day is linearly related to the amount of sinks produced in a day, derive the total cost function of the company? 2. Find a function for the average cost of this company
The demand equation for your company's virtual reality video headsets is 1,500 p = g0.3 where g is the total number of headsets that your company can sell in a week at a price of p dollars. The total manufacturing and shipping cost amounts to $110 per headset. (a) Find the weekly cost, revenue and profit as a function of the demand q for headsets. C(q)= 110g R(q)= 1500g0.7 P(g)= 1500 g0. – 1109 (b) How many headsets should your company sell to maximize profit? (Give your answer to the nearest whole number.) q = 1845 V headsets What is the greatest profit your company can make in a week? (Give your answer to the nearest whole number.) $ E Second derivative test: Your answer above is a critical point for the weekly profit function. To show it is a maximum, calculate the second derivative of the profit function. P"(q)= 86977 Evaluate P"(qg) at your critical point. The result is negative , which means that the profit is concave down v at the critical point, and the critical point is a…

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