Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Related questions
Topic Video
Question
A furniture manufacturer builds tables. The cost for materials and labor to build a kitchen table is $240 and the profit is $160. The cost to build a dining room table is $320 and the profit is $240. Let x represent the number of kitchen tables produced per month. Let y represent the number of dining room tables produced per month.
a. Write an objective function representing the monthly profit for producing and selling x kitchen tables and y dining room tables.
b.The manufacturing process is subject to the following constraints. Write a system of inequalities representing the constraints.
• The number of each type of table cannot be negative.
• Due to labor and equipment restrictions, the company can build at most 120 kitchen tables.
• The company can build at most 90 dining room tables.
• The company does not want to exceed a monthly cost of $48,000.
c. Graph the system of inequalities represented by the constraints.
d. Find the vertices of the feasible region
e. Test the objective function at each vertex.
f. How many kitchen tables and how many dining room tables should be produced to maximize profit? (Assume that all tables produced will be sold.)
g. What is the maximum profit?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 7 steps with 7 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Similar questions
- T? day, of wide. graph. rent the same machine for $28 plus $4 per many hours of use will the total amount spent at each company be the same? What will be the total amount spent at each company? 31. Taxi rates are determined by local authorities. In New York City, the night-time cost of a taxi includes a base fee of $3 plus a charge of $1.56 per kilometer. In Boston, regardless of the time of day, the base fee is $2.60 with a charge of $1.75 per kilometer. For how many kilometers will the cost of a night-time taxi ride in each city be the same? Round to the nearest kilometer. What will the cost be in each city for the rounded number of kilometers? 3 39 40.arrow_forward5. A small company makes baseball caps. The graph shows how the cost, sales, and profit change as the number of caps produced increases. 80 40 20 . efit! Caps produced (1000) -20 a) Describe each relationship. Explain your reasoning. i) The relationship between the cost and the number of caps produced. ii) The relationship between the profit and the number of caps produced. b) Describe how the manager might decide how many caps to produce based on the graph. (o001S) junowyarrow_forwardTwo friends, Parker and David, took summer jobs. The graph below represents David's earnings in dollars and cents, y, for working x hours. David's Earnings S600 $550 $500 $450 $400 (20,$406) $350 $300 $250 $200 (10,$203) S150 $100 $50 5 15 25 30 35 40 45 50 55 Hours Worked The table below represents Parker's earnings in dollars and cents, y, for working a hours. Parker's Earnings Hours (x) Earnings (y) 10 $226 15 $339 20 $452 25 $565 Use the dropdown menu and answer- blank below to form a true statement. Parker earns $ per hour than David. Submit Answer Earnings (Dollars)arrow_forward
- It costs $1000 to produce 100 t-shirts in a day, and it costs $1300 to produce 140 t-shirts in a day. Assume that the daily cost is a linear function of the number of t-shirts produced per day.a. Determine the marginal cost per t-shirt.b. Determine the fixed daily cost.arrow_forwardA contractor purchases a backhoe for $37, 300. Fuel and standard maintenance cost $5.95 per hour, and the operator is paid $12.03 per hour. a. Write a cost function for the cost C(z) of operating the backhoe for hours. Be sure to include the purchase price in the cost function. Cost function: C(z) = dollars b. If customers pay $27.77 per hour for the contractor's backhoe service, write the revenue function R(z) for the amount of revenue gained from a hours of use. Revenue function: R(x) = I c. Write the profit function P(x) for the amount of profit gained from a hours of use. Profit function: P(x) = dollars dollars d. How many hours must the backhoe be used in order to break even (assume that part of an hour counts as a whole hour)? In order for the contractor to break even, customers need to pay to use the backhoe for a total of hours.arrow_forward7. Sky Launch Trampoline Park charges Customers $9.50 per hour they spend jumping. Each customer must also pay $2.50 for grip socks. Write an equation in slope-intercept form to represent this linear function. Derrick spent $31 at Sky Launch Trampoline Park on Sunday. How many hours did he jump?arrow_forward
- It costs a company $3,500 to produce 3,000 pencils whereas it costs the company $1,500a month even if they don't produce any pencils. If they sell the pencils for $0.75 and thecost, revenue, and profit functions are linear, determine how many pencils they must makein a month to break evenarrow_forwardThe circle graph shows how a company's annual budget of $11,000,000 is divided by department. First decide whether the company budgets more for media, more for support, or the same amount for each. Media: 31% Sales: 13% Research: 9% Marketing: 16% Support: 22% Editorial: 9%arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSON
Contemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage Learning
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning 
Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSON
Introduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge Press
College Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:9781305657960
Author:Joseph Gallian
Publisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:9780135163078
Author:Michael Sullivan
Publisher:PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:9780980232776
Author:Gilbert Strang
Publisher:Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:9780077836344
Author:Julie Miller, Donna Gerken
Publisher:McGraw-Hill Education