Stefan is an exchange student from Germany who works at a local theme park drawing caricatures of the tourists visiting the park. He provides all of his own materials but pays a booth rental fee. The cost of operating his caricature art business is given by the function C(x) = 0.5(x - 25)2 + 60 dollars, where x is the number of caricatures drawn, and x ≥ 0. a. Choose the vertex of the cost function and interpret using a complete sentence. O (0.5, -25); The cost of operating his caricature art business is decreasing by 25. O (60, 25); To minimize his costs Stefan must draw 60 caricatures. O (0, 60); To minimize his costs Stefan must draw 60 caricatures. O (25, 60); To minimize his costs Stefan must draw 25 caricatures. b. How many caricatures must he draw to minimize his costs? Number c. State the minimum total cost. Number d. Graph the function C(x) = 0.25(x - 10)2 + 30 by hand. (C(x) values are labeled in y-axis and x values are labeled in x-axis)

Stefan is an exchange student from Germany who works at a local theme park drawing caricatures of the tourists visiting the park. He provides all of his own materials but pays a booth rental fee. The cost of operating his caricature art business is given by the function C(x) = 0.5(x - 25)2 + 60 dollars, where x is the number of caricatures drawn, and x ≥ 0. a. Choose the vertex of the cost function and interpret using a complete sentence. O (0.5, -25); The cost of operating his caricature art business is decreasing by 25. O (60, 25); To minimize his costs Stefan must draw 60 caricatures. O (0, 60); To minimize his costs Stefan must draw 60 caricatures. O (25, 60); To minimize his costs Stefan must draw 25 caricatures. b. How many caricatures must he draw to minimize his costs? Number c. State the minimum total cost. Number d. Graph the function C(x) = 0.25(x - 10)2 + 30 by hand. (C(x) values are labeled in y-axis and x values are labeled in x-axis)

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Similar questions

Please help with the attached word problem & rational equation. Thank you.
An insurance company claims that for x thousand policies, its monthly revenue in dollars is given by R(x) = 160x and its monthly cost in dollars is given by C(x) = 120x+9,600. a. Find the break-even point. b. Graph the revenue and cost equations on the same axes. c. From the graph, estimate the revenue and cost when x = 120.
Company A sells floor tiles which are 2 square feet in area, weigh 4 pounds, and cost $1. Company B sells floor tiles which are 3 square feet in area, weigh 2 pounds, and cost $2. Your job is to buy floor tiles to maximize the area covered, at a total cost of no more than $10 and a total weight of no more than 16 pounds. Please use the graph paper. Let X be the number of tiles from Company A, and Y be the number of tiles from Company B. Show your work. How many tiles do you buy from Company A? _______ How many tiles do you buy from Company B? _______
A sandwich store's weekly revenue is given by the function R(x) = -0.0001 x2 + 3 x. The graph of the revenue function has a minimum value of 15,000. True False
The owner of an apartment building has 100 apartments. He has found that if he charges $500 per month he can rent all 100 of them but he rents one fewer apartment for each $25 increase in monthly rent. a. Write an equation that gives the monthly revenue from the rental of the apartments if he makes x increases of $25 in the rent. b. Find the rent he should charge to maximize the monthly revenue and the number of apartments he will rent by charging this amount. c. Suppose the landlord pays for water, sewer, and electricity at his apartments for a cost of $50 per apartment per month. Write an equation that gives the monthly cost to the landlord after x price increases of $25. d. Write an equation that gives the monthly profit the landlord makes, and the rent he should charge to maximize his monthly profit, and the number of apartments he will rent by charging this amount. e. Explain why you know mathematically your solutions to (2) and (4) are maximum values. f. In a sentence or two…
The marketing department of a company estimates that the demand for a product is given by p = 100 - 0.0001x, where p is the price per unit and x is the number of units. The cost C of producing x units is given by C = 310,000 + 25x and the profit P for producing and selling x units is given by P = R - C = xp – C. Sketch the graph of the profit function. P FA 15 000 000 15 000 000 10 000 000 10 000 000 5 000 000 5000 000 1 2 3 4 5 7 8 9 1 2 3 4 5 6 8 9 1 = 100,000 1= 100,000 MacBook DII 888 F9 F8 F7 F4 F5 F3 F1 * & $ % @ # 8 9 2 3 4 T Y Q W K G H .. . - < (O
An insurance company claims that for x thousand policies, its monthly revenue in dollars is given by R(x)=100x and its monthly cost in dollars is given by C(x)=75x+3,750 a. Find the break-even point. b. Graph the revenue and cost equations on the same axes. c. From the graph, estimate the revenue and cost when x=75
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 $
Describe the graph of the quadratic function; f(x)= −4 (x − 8)2 + 4.