College Algebra
10th Edition
ISBN: 9781337282291
Author: Ron Larson
Publisher: Cengage Learning
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Question
Chapter 6.5, Problem 60E
(a)
To determine
To graph: The system of inequalities for the demand and supply equations of consumer surplus and producer surplus.
(b)
To determine
To calculate: The consumer surplus and producer surplus.
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em Solving and Business Applications Using Systems of Equar
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2. A company that manufactures small canoes has a fixed cost of $18,000. It cost $20 to
produce each canoe. The selling price is $80 per canoe. Let x represent the number of
canoes produced and sold.
a) What is the cost function?
b) What is the revenue function?
99+
a
eby
The table below gives the quantity of dental extractors
demanded and the quantity supplied for selected prices.
(a) Find the linear equation that gives the price as a
function of the quantity demanded.
(b) Find the linear equation that gives the price as a
function of the quantity supplied.
(c) Use these equations to find the market equilibrium
price.
Price
Quantity
($) Demanded (thousands) Supplied (thousands)
20
30
40
50
100
Quantity
765
715
665
615
365
0
400
800
1200
3200
C
(a) What is the price as a function of the
quantity demanded?
p=
(Type an expression using q as the variable. Type
your answer in slope-intercept form.)
(b) What is the price as a function of the
quantity supplied?
p=
(Type an expression using q as the variable. Type
your answer in slope-intercept form.)
(c) What is the market equilibrium price?
$
Chapter 6 Solutions
College Algebra
Ch. 6.1 - Solve the system of equations. xy=05x3y=6Ch. 6.1 - A total of $25,000 is invested in two funds paying...Ch. 6.1 - Solve the system of equations. 2x+y=5x2y+3x=1Ch. 6.1 - Solve the system of equations. 2x+y=32x2+4xy2=0Ch. 6.1 - Prob. 5ECPCh. 6.1 - Prob. 6ECPCh. 6.1 - Prob. 7ECPCh. 6.1 - Prob. 1ECh. 6.1 - Prob. 2ECh. 6.1 - Fill in the blanks. Graphically, solutions of a...
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Two systems of equations that...Ch. 6.2 - Prob. 3ECh. 6.2 - Prob. 4ECh. 6.2 - Solving a System by Elimination In Exercises 5-12,...Ch. 6.2 - Solving a System by Elimination In Exercises 5-12,...Ch. 6.2 - Solving a System by Elimination In Exercises 5-12,...Ch. 6.2 - Prob. 8ECh. 6.2 - Solving a System by Elimination In Exercises 5-12,...Ch. 6.2 - Solving a System by Elimination In Exercises 5-12,...Ch. 6.2 - Solving a System by Elimination In Exercises 5-12,...Ch. 6.2 - Solving a System by Elimination In Exercises 5-12,...Ch. 6.2 - Solving a System by Elimination In Exercises...Ch. 6.2 - Solving a System by Elimination In Exercises...Ch. 6.2 - Solving a System by Elimination In Exercises...Ch. 6.2 - Solving a System by Elimination In Exercises...Ch. 6.2 - Solving a System by Elimination In Exercises...Ch. 6.2 - Prob. 18ECh. 6.2 - Solving a System by Elimination In Exercises...Ch. 6.2 - Prob. 20ECh. 6.2 - Prob. 21ECh. 6.2 - Solving a System by Elimination In Exercises...Ch. 6.2 - Prob. 23ECh. 6.2 - Prob. 24ECh. 6.2 - Prob. 25ECh. 6.2 - Prob. 26ECh. 6.2 - Solving a System by Elimination In Exercises...Ch. 6.2 - Prob. 28ECh. 6.2 - Prob. 29ECh. 6.2 - Prob. 30ECh. 6.2 - Matching a System with Its Graph In Exercises...Ch. 6.2 - Prob. 32ECh. 6.2 - Matching a System with Its Graph In Exercises...Ch. 6.2 - Prob. 34ECh. 6.2 - Prob. 35ECh. 6.2 - Prob. 36ECh. 6.2 - Choosing a Solution Method In Exercises 35-40, use...Ch. 6.2 - Choosing a Solution Method In Exercises 35-40, use...Ch. 6.2 - Prob. 39ECh. 6.2 - Prob. 40ECh. 6.2 - Airplane Speed An airplane flying into a headwind...Ch. 6.2 - Airplane Speed Two planes start from Los Angeles...Ch. 6.2 - Nutrition Two cheeseburgers and one small order of...Ch. 6.2 - Nutrition One eight-ounce glass of apple juice and...Ch. 6.2 - Prob. 45ECh. 6.2 - Finding the Equilibrium Point In Exercises 45-48,...Ch. 6.2 - Prob. 47ECh. 6.2 - Prob. 48ECh. 6.2 - Chemistry Thirty liters of a 40% acid solution is...Ch. 6.2 - Fuel Mixture Five hundred gallons of 89-octane...Ch. 6.2 - 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Prob. 22ECh. 6.5 - Prob. 23ECh. 6.5 - Graphing an Inequality In Exercises 19-26, use a...Ch. 6.5 - Prob. 25ECh. 6.5 - Prob. 26ECh. 6.5 - Prob. 27ECh. 6.5 - Writing an Inequality In Exercises 27-30, write an...Ch. 6.5 - Writing an Inequality In Exercises 27-30, write an...Ch. 6.5 - Writing an Inequality In Exercises 27-30, write an...Ch. 6.5 - Prob. 31ECh. 6.5 - Prob. 32ECh. 6.5 - Prob. 33ECh. 6.5 - Prob. 34ECh. 6.5 - Prob. 35ECh. 6.5 - Prob. 36ECh. 6.5 - Prob. 37ECh. 6.5 - Prob. 38ECh. 6.5 - Prob. 39ECh. 6.5 - Prob. 40ECh. 6.5 - Prob. 41ECh. 6.5 - Prob. 42ECh. 6.5 - Prob. 43ECh. 6.5 - Prob. 44ECh. 6.5 - Prob. 45ECh. 6.5 - Prob. 46ECh. 6.5 - Prob. 47ECh. 6.5 - Prob. 48ECh. 6.5 - Prob. 49ECh. 6.5 - Prob. 50ECh. 6.5 - Prob. 51ECh. 6.5 - Prob. 52ECh. 6.5 - Writing a System of Inequalities In Exercises...Ch. 6.5 - Writing a System of Inequalities In Exercises...Ch. 6.5 - Prob. 55ECh. 6.5 - Writing a System of Inequalities In Exercises...Ch. 6.5 - Prob. 57ECh. 6.5 - Prob. 58ECh. 6.5 - Consumer Surplus and Producer Surplus In Exercises...Ch. 6.5 - 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- Consumer Surplus and Producer Surplus In Exercises 83 and 84, (a) graph the systems of inequalities representing the consumer surplus and producer surplus for the supply and demand equations and (b) find the consumer surplus and producer surplus. Demand Supply p=1600.0001x p=70+0.0002xarrow_forwardBreak-Even Analysis In Exercises 55 and 56, use the equations for the total cost C and total revenue R to find the number x of units a company must sell to break even. (Round to the nearest whole unit.) C=8650+250,000,R=9502xarrow_forwardRedo Exercise 5, assuming that the house blend contains 300 grams of Colombian beans, 50 grams of Kenyan beans, and 150 grams of French roast beans and the gourmet blend contains 100 grams of Colombian beans, 350 grams of Kenyan beans, and 50 grams of French roast beans. This time the merchant has on hand 30 kilograms of Colombian beans, 15 kilograms of Kenyan beans, and 15 kilograms of French roast beans. Suppose one bag of the house blend produces a profit of $0.50, one bag of the special blend produces a profit of $1.50, and one bag of the gourmet blend produces a profit of $2.00. How many bags of each type should the merchant prepare if he wants to use up all of the beans and maximize his profit? What is the maximum profit?arrow_forward
- System of Linear Equations. In Exercises 57-62, use a software program or a graphing utility to solve the system of linear equations. 123.5x+61.3y32.4z=262.7454.7x45.6y+98.2z=197.442.4x89.3y+12.9z=33.66arrow_forwardInventory Costs A warehouse operator has 24,000 square feet of floor space in which to store two products. Each unit of product I requires 20 square feet of floor space and costs $12 per day to store. Each unit of product II requires 30 square feet of floor space and costs $8 per day to store. The total storage cost per day cannot exceed $12,400. Write and graph a system that describes all possible inventory levels.arrow_forwardSubject-advance mathsarrow_forward
- A cleaning company charges $100 for each office it cleans. The fixed monthly cost of $480 for the company includes telephone service and the depreciation on cleaning equipment and a van. The variable cost is $60 per office and includes labor, gasoline, and cleaning supplies. (a) Write a linear cost function representing the cost C (x) (in $) to clean x offices per month. (b) Write a linear revenue function representing the revenue R (x) (in $) for cleaning x offices per month. (c) Determine the number of offices to be cleaned per month for the company to break even. (d) If 10 offices are cleaned, will the company make money or lose money?arrow_forwardAn athlete is planning a diet change for training. Each time he eats meal A he gets 20 grams of protein and 30 grams of carbohydrates. Each meal B provides 20 grams of protein and 50 grams of carbohydrates. Each meal A costs $5 each and each meal B costs $7.5. The athlete needs at least 80 grams of protein and 160 grams of carbohydrates. (A) let x be the number of meal A and y be the number of meal B. write inequalities for this linear programming problem. (B) identify the feasible set (C) Minimize the objective function 5x+7.5y (the total cost)arrow_forwardThe owner of a restaurant franchise pays the parent company a monthly fee of $5057 plus 18% of sales. (a) Write a linear model to compute the monthly payment, y, that the restaurant owner must pay the parent company for x dollars in sales. (b) Use the equation from part(a) to compute the amount that the owner has to pay if monthly sales are $10,200. Part: 0/2 Part 1 of 2 (a) Write a linear model to compute the monthly payment, y, that the restaurant owner must pay the parent company for x dollars in sales. y = Skip Part Check Answer Save For Later Submit Assignment 62021 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center NOV 6.arrow_forward
- The table below gives the quantity of electronic sensors demanded and the quantity supplied for selected prices. (a) Find the linear equation that gives the price as a function of the quantity demanded. (b) Find the linear equation that gives the price as a function of the quantity supplied. (c) Use these equations to find the market equilibrium price. Price ($) 20 CRAWNG 30 40 50 100 Quantity Demanded (thousands) 650 600 550 500 250 Quantity Supplied (thousands) 0 200 400 600 1600 COTTES (a) What is the price as a function of the quantity demanded? P=0 (Type an expression using q as the variable. Type your answer in slope-intercept form.) (b) What is the price as a function of the quantity supplied? p= (Type an expression using q as the variable. Type your answer in slope-tercept form.) (c) What is the market equilibrium price?arrow_forward(Figure: The Blu-ray Disc Rental Market) Use Figure: The Blu-ray Disc Rental Market. At a rental price of $6, there will be: Question 6 options: an excess demand of 20 Blu-ray disc rentals. equilibrium in the rental market for Blu-ray discs. an excess supply of 20 Blu-ray disc rentals. a decrease in demand.arrow_forward
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