The total revenue function for a product isgiven byR=655xdollars, and the total cost function for thissame product is given byC=19,250+70x+x2,where C is measured in dollars. For bothfunctions, the input x is the number of unitsproduced and sold.a. Form the profit function for this productfrom the two given functions.b. What is the profit when25units are produced and sold?c. What is the profit when43units are produced and sold?

A profit function is a mathematical relationship between a firm's total profit and output. It equals…

Answered: C=19,250+70x+x2, where C is measured in…

C=19,250+70x+x2, where C is measured in dollars. For both unctions, the input x is the number of unit produced and sold. a. Form the profit function for this product

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.7P

See similar textbooks

Similar questions

Which costs are measured on per-unit basis: fixed costs, average cost, avenge variable cost, variable costs, and marginal cost?
Break-Even The total revenue function for Frenchdoor refrigerators is given by R = 550x dollars, andthe total cost function for this same product is givenby C = 10,000 + 30x + x2, where C is measured indollars. For both functions, the input x is the numberof refrigerators produced and sold.a. Form the profit function for the refrigerators fromthe two given functions. b. What is the profit when 18 refrigerators areproduced and sold?c. What is the profit when 32 refrigerators areproduced and sold?d. How many refrigerators must be sold to breakeven on this product?
If company A manufactures t-shirts and sells them to retailers for US$9.80 each.It has fixed costs of $2625 related to the production of the t-shirts, and the production cost perunit is US$2.30. Company B also manufactures t-shirts and selll them directly to consumers.The demand for its product is p = 15 −x125 , its production cost per unit is US$5.00and its fixed cost are the same as for company A . (vii) Derive the total revenue function,R(x) for company B.(viii) Derive the profit function,Π(x) for company B.(ix) How many t-shirts must company B sell to in order to break-even.(x) How many t-shirts must company B sell to maximise its profit
If company A manufactures t-shirts and sells them to retailers for US$9.80 each.It has fixed costs of $2625 related to the production of the t-shirts, and the production cost perunit is US$2.30. Company B also manufactures t-shirts and sell them directly to consumers.The demand for its product is p = 15 −x 125, its production cost per unit is US$5.00and its fixed cost are the same as for company A.(i) Derive the total revenue function, R(x) for company A.(ii) Derive the total cost function, C(x) for company A.(iii) Derive the profit function, Π(x) for company A.(iv) Using a spreadsheet, create a table for showing x, R(x)?, C(x) for company Ain the domain x = 50, 100, 150, 200, 250, 300, 350, 400, 450.(v) Graph the functions from (d) above on the same axes.(vi) From your graph, determine the break-even level of output for company A.(vii) Derive the total revenue function, R(x) for company B.(viii) Derive the profit function,…
Maximization Profit The total weekly revenue (in dollars) of the Country Workshop realized in manufacturing and selling its rolltop desks is given byR (x, y) = −0.1x2−- 0.25y2 − 0.2xy + 200x + 160ywhere x denotes the number of finished units and y denotes the number of unfinished units manufactured and sold each week. The total weekly cost attributable to the manufacture of these desks is given byC (x, y)= 100x + 70y + 4000dollars. Determine how many finished units and how many unfinished units the company should manufacture each week to maximize its profit. What is the maximum profit realizable?
Suppose a company has fixed costs of $300 and variable costs of 3/4 x+1460 dollars per unit, where x is thetotal number of units produced. Suppose further that the selling price of its product is 1500−1/4 x dollars per unit.(a) Find the break-even points.(b) Find the maximum revenue.(c) Form the profit function from the cost and revenue functions and find maximum profit.(d) What price will maximize the profit?
Revenue and Cost The total revenue function for LED TVs is given by R = 1050x dollars, and the total cost function for the TVs isC = 10,000 + 30x + x2dollars, where x is thenumber of TVs that are produced and sold.a. Which function is quadratic, and which is linear? b. Form the profit function for the TVs from thesetwo functions.c. Is the profit function a linear function, a quadraticfunction, or neither of these?
The Rainwater Brewery produces beer. The annual fixed cost is $150,000, and the variable cost perbarrel is $16. Price is related to demand according to the following linear equation.v -75,000 1,153.8pDevelop the nonlinear profit function for the brewery and determine the price that will max-imize profit, the optimal volume, and the maximum profit per year.
A company produces and sells a product and fixed costs of the company are 8500000 Baisa and variable cost is RO. (35+K) per unit and sells the product at RO. (70+M) per unit.a. Find the total cost function. b. Find the total revenue function. c. Find the profit function and determine the profit when 1250 units are sold. d. How many units must be produced and sold to yield a profit of RO. 20000? e. How many units must be sold to break even?
A company makes solar panels. The company’s revenue function, in dollars, is R(n)=10n , where n is the number of panels produced. The cost function is C(n)=100(2)π/30 . R and C are shown on the graphbelow. a) Estimate from the graph i) the break-even points ii) the number of panels that should be produced for maximum profit b) Write the equation for the profit function P. c) Graph P. d) Use your graph of P to estimate the number of panels that give maximum profit. e) How would your answers for break-even points and maximum profit change if i) the number of dollars of revenue per panel is increased slightly? ii) the cost function is C(n)=100(2)π/35 changed to ? f) What does the number that was changed in part e) ii) represent?
If company A manufactures t-shirts and sells them to retailers for US$9.80 each. It has fixed costs of $2625 related to the production of the t-shirts, and the production cost per unit is US$2.30. Company B also manufactures t-shirts and selll them directly to consumers.The demand for its product is p = 15 −x 125, its production cost per unit is US$5.00 and its fixed cost are the same as for company A . (i) Derive the total revenue function, R(x) for company A. (ii) Derive the total cost function, C(x) for company A. (iii) Derive the profit function, Π(x) for company A. (iv) Using a spreadsheet, create a table for showing x, R(x)?, C(x) for company A in the domain x = 50, 100, 150, 200, 250, 300, 350, 400, 450.(v) Graph the functions from (d) above on the same axes. (vi) From your graph, determine the break-even level of output for company A. (vii) Derive the total revenue function, R(x) for company B. (viii) Derive the profit…
2. J&J Company is considering publishing a paperback textbook on spreadsheet applications for business. The fixed cost of manuscript preparation, textbook design, and production setup is estimated to beP100,000. Variable production and material costs are estimated to be P150 per book. Demand over the life of the book is estimated to be 4000 copies. The publisher plans to sell the text to college and university bookstores forP1000 each. REQUIRED: a. Formulate the total cost function. b. Formulate the revenue function. c. Formulate the profit function. d. What is the breakeven point? e. What profit or loss can be anticipated with a demand of 4000 copies? f. With a demand of 4000 copies, what is the minimum price per copy that the publisher must charge to break even? g. If the publisher believes that the price per copy could be increased to P1, 297. 50 and would not affect the anticipated demand of 4000 copies, what action would you recommend? h. What profit or loss can be…