College Algebra
10th Edition
ISBN: 9781337282291
Author: Ron Larson
Publisher: Cengage Learning
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Chapter 6.6, Problem 28E
To determine
To calculate: The maximum and minimum values of the provided objective function
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Students have asked these similar questions
Q6: Create a model using an Algebraic Constraint block to find a solution
for the non-linear equation:
F(x) = 3x-2x + 6x – 8
The decision variables represent the amounts of ingredients 1, 2, and 3 to put into a blend. The objective function represents profit. The first three constraints measure the usage and availability of resources A, B, and C. The fourth constraint is a minimum requirement for ingredient 3. Use the output to answer these questions.
a.
How much of ingredient 1 will be put into the blend?
b.
How much of ingredient 2 will be put into the blend?
c.
How much of ingredient 3 will be put into the blend?
d.
How much resource A is used?
e.
How much resource B will be left unused?
f.
What will the profit be?
g.
What will happen to the solution if the profit from ingredient 2 drops to 4?
h.
What will happen to the solution if the profit from ingredient 3 increases by 1?
i.
What will happen to the solution if the amount of resource C increases by 2?
j.
What will happen to the solution if the minimum requirement for ingredient 3 increases to 15?
LINEAR PROGRAMMING…
Read the information below and construct the objective function, and the associated constraint
inequalities. DO NOT SOLVE THE MINIMUM PROBLEM.
The liquid portion of a diet is to provide at least 380 calories, at least 80 units of vitamin A, and
at least 140 units of vitamin C daily. A cup of dietary drink X provides 50 calories, 20 units
of vitamin A, and 30 units of vitamin C. A cup of dietary drink Y provides 40 calories, 30
units of vitamin A, and 90 units of vitamin C. Dietary drink X costs $0.24 per cup and drink
Y costs $0.31 per cup.
Construct the objective function for minimizing the cost, and construct the associated constraint
inequalities to meet the daily dietary requirements by selecting the appropriate symbol or number
from the dropdown list.
Note: The symbol = in
the dropdown list indicates "greater than or equal to".
Cost
=
[Select]
[Select]
20X+ [Select]
[Select]
X+ [Select ]
X + 40Y [Select]
✓Y [Select]
X + 90Y [Select]
✓ Y
✓380
80
140
Chapter 6 Solutions
College Algebra
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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 - 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Prob. 62ECh. 6.3 - Geometry The perimeter of a triangle is 180 feet....Ch. 6.3 - Chemistry A chemist needs 10 liters of a 25 acid...Ch. 6.3 - Electrical Network Applying Kirchhoff’s Laws to...Ch. 6.3 - Pulley System A system of pulleys is loaded with...Ch. 6.3 - Prob. 67ECh. 6.3 - Prob. 68ECh. 6.3 - Prob. 69ECh. 6.3 - Prob. 70ECh. 6.3 - Prob. 71ECh. 6.3 - Prob. 72ECh. 6.3 - Prob. 73ECh. 6.3 - Prob. 74ECh. 6.3 - Prob. 75ECh. 6.3 - The number of sides x and the combined number of...Ch. 6.3 - Prob. 77ECh. 6.3 - Prob. 78ECh. 6.3 - Prob. 79ECh. 6.3 - Prob. 80ECh. 6.4 - Write the partial fraction decomposition of...Ch. 6.4 - Prob. 2ECPCh. 6.4 - Prob. 3ECPCh. 6.4 - Write the partial fraction decomposition of...Ch. 6.4 - Prob. 5ECPCh. 6.4 - Prob. 1ECh. 6.4 - Prob. 2ECh. 6.4 - Prob. 3ECh. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - Prob. 6ECh. 6.4 - Matching In Exercises 5-8, match the rational...Ch. 6.4 - Prob. 8ECh. 6.4 - Writing the Form of the Decomposition In Exercises...Ch. 6.4 - Prob. 10ECh. 6.4 - Writing the Form of the Decomposition In Exercises...Ch. 6.4 - Writing the Form of the Decomposition In Exercises...Ch. 6.4 - Writing the Form of the Decomposition In Exercises...Ch. 6.4 - Prob. 14ECh. 6.4 - Writing the Form of the Decomposition In Exercises...Ch. 6.4 - Prob. 16ECh. 6.4 - Writing the Partial Fraction Decomposition In...Ch. 6.4 - Prob. 18ECh. 6.4 - Writing the Partial Fraction Decomposition In...Ch. 6.4 - Prob. 20ECh. 6.4 - Writing the Partial Fraction Decomposition In...Ch. 6.4 - Prob. 22ECh. 6.4 - Prob. 23ECh. 6.4 - Prob. 24ECh. 6.4 - Prob. 25ECh. 6.4 - Prob. 26ECh. 6.4 - Prob. 27ECh. 6.4 - Prob. 28ECh. 6.4 - Prob. 29ECh. 6.4 - Prob. 30ECh. 6.4 - Prob. 31ECh. 6.4 - Prob. 32ECh. 6.4 - Prob. 33ECh. 6.4 - Prob. 34ECh. 6.4 - Prob. 35ECh. 6.4 - Prob. 36ECh. 6.4 - Prob. 37ECh. 6.4 - Prob. 38ECh. 6.4 - Prob. 39ECh. 6.4 - Prob. 40ECh. 6.4 - Prob. 41ECh. 6.4 - Prob. 42ECh. 6.4 - Prob. 43ECh. 6.4 - Prob. 44ECh. 6.4 - Prob. 45ECh. 6.4 - Prob. 46ECh. 6.4 - Prob. 47ECh. 6.4 - Prob. 48ECh. 6.4 - Prob. 49ECh. 6.4 - Prob. 50ECh. 6.4 - Prob. 51ECh. 6.4 - Prob. 52ECh. 6.4 - Prob. 53ECh. 6.4 - Prob. 54ECh. 6.4 - Prob. 55ECh. 6.4 - Prob. 56ECh. 6.4 - Prob. 57ECh. 6.4 - Prob. 58ECh. 6.4 - Environmental Science The predicted cost C (in...Ch. 6.4 - Thermodynamics The magnitude of the range R of...Ch. 6.4 - Prob. 61ECh. 6.4 - Prob. 62ECh. 6.4 - Prob. 63ECh. 6.4 - HOW DO YOU SEE IT? Identify the graph of the...Ch. 6.4 - Error Analysis Describe the error in writing the...Ch. 6.4 - Prob. 66ECh. 6.5 - Sketch the graph of x+22+y2216.Ch. 6.5 - Sketch the graph of x3.Ch. 6.5 - Prob. 3ECPCh. 6.5 - Sketch the graph of the solution set of the system...Ch. 6.5 - Prob. 5ECPCh. 6.5 - Sketch the solution set of the system of...Ch. 6.5 - Sketch the solution set of the system of...Ch. 6.5 - The demand and supply equations for a flat-screen...Ch. 6.5 - Prob. 9ECPCh. 6.5 - Prob. 1ECh. 6.5 - Prob. 2ECh. 6.5 - Prob. 3ECh. 6.5 - Prob. 4ECh. 6.5 - Prob. 5ECh. 6.5 - Graphing an Inequality In Exercises 5-18, sketch...Ch. 6.5 - Prob. 7ECh. 6.5 - Prob. 8ECh. 6.5 - Prob. 9ECh. 6.5 - Prob. 10ECh. 6.5 - Prob. 11ECh. 6.5 - Graphing an Inequality In Exercises 5-18, sketch...Ch. 6.5 - Prob. 13ECh. 6.5 - Prob. 14ECh. 6.5 - Prob. 15ECh. 6.5 - Graphing an Inequality In Exercises 5-18, sketch...Ch. 6.5 - Prob. 17ECh. 6.5 - Prob. 18ECh. 6.5 - Prob. 19ECh. 6.5 - Prob. 20ECh. 6.5 - Prob. 21ECh. 6.5 - 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 - Prob. 60ECh. 6.5 - Prob. 61ECh. 6.5 - Prob. 62ECh. 6.5 - Prob. 63ECh. 6.5 - Ticket Sales For a concert event, there are $30...Ch. 6.5 - Production A furniture company produces tables and...Ch. 6.5 - Prob. 66ECh. 6.5 - Nutrition A dietician prescribes a special dietary...Ch. 6.5 - Prob. 68ECh. 6.5 - Shipping A warehouse supervisor has instructions...Ch. 6.5 - Physical Fitness Facility A physical fitness...Ch. 6.5 - Prob. 71ECh. 6.5 - Prob. 72ECh. 6.5 - Prob. 73ECh. 6.5 - Prob. 74ECh. 6.5 - Matching Match the system of inequalities with the...Ch. 6.5 - Prob. 76ECh. 6.6 - Find the maximum value of z=4x+5y subject to the...Ch. 6.6 - Find the minimum value of z=12x+8y Where x0 and...Ch. 6.6 - Find the maximum value of z=12x+8y Where x0 and...Ch. 6.6 - Find the minimum value of z=3x+7y Where x0 and y0,...Ch. 6.6 - In Example 5, the candy manufacturer improves the...Ch. 6.6 - Prob. 6ECPCh. 6.6 - Prob. 1ECh. 6.6 - Prob. 2ECh. 6.6 - Prob. 3ECh. 6.6 - Prob. 4ECh. 6.6 - Prob. 5ECh. 6.6 - Prob. 6ECh. 6.6 - Prob. 7ECh. 6.6 - Prob. 8ECh. 6.6 - Prob. 9ECh. 6.6 - Prob. 10ECh. 6.6 - Prob. 11ECh. 6.6 - Prob. 12ECh. 6.6 - Prob. 13ECh. 6.6 - Solving a Linear Programming Problem In Exercises...Ch. 6.6 - Prob. 15ECh. 6.6 - Prob. 16ECh. 6.6 - Prob. 17ECh. 6.6 - Prob. 18ECh. 6.6 - Prob. 19ECh. 6.6 - Prob. 20ECh. 6.6 - Prob. 21ECh. 6.6 - Prob. 22ECh. 6.6 - Prob. 23ECh. 6.6 - Prob. 24ECh. 6.6 - Prob. 25ECh. 6.6 - Prob. 26ECh. 6.6 - Prob. 27ECh. 6.6 - Prob. 28ECh. 6.6 - Prob. 29ECh. 6.6 - Prob. 30ECh. 6.6 - Prob. 31ECh. 6.6 - Prob. 32ECh. 6.6 - Prob. 33ECh. 6.6 - Prob. 34ECh. 6.6 - Prob. 35ECh. 6.6 - Prob. 36ECh. 6.6 - Optimal Profit A merchant plans to sell two models...Ch. 6.6 - Optimal Profit A manufacturer produces two models...Ch. 6.6 - Optimal Cost A public aquarium is adding coral...Ch. 6.6 - Optimal Labor A manufacturer has two different...Ch. 6.6 - Optimal Revenue An accounting firm has 780 hours...Ch. 6.6 - Prob. 42ECh. 6.6 - Agriculture A fruit grower raises crops A and B....Ch. 6.6 - Prob. 44ECh. 6.6 - Prob. 45ECh. 6.6 - Prob. 46ECh. 6.6 - Prob. 47ECh. 6.6 - Prob. 48ECh. 6.6 - Prob. 49ECh. 6.6 - Prob. 50ECh. 6.6 - Prob. 51ECh. 6 - Solving a System by Substitution In Exercises...Ch. 6 - Solving a System by Substitution In Exercises...Ch. 6 - Prob. 3RECh. 6 - Prob. 4RECh. 6 - Prob. 5RECh. 6 - Prob. 6RECh. 6 - Prob. 7RECh. 6 - Prob. 8RECh. 6 - Prob. 9RECh. 6 - Prob. 10RECh. 6 - Prob. 11RECh. 6 - Solving a System of Equations Graphically In...Ch. 6 - Solving a System of Equations Graphically In...Ch. 6 - Prob. 14RECh. 6 - Prob. 15RECh. 6 - Prob. 16RECh. 6 - Prob. 17RECh. 6 - Prob. 18RECh. 6 - Prob. 19RECh. 6 - Prob. 20RECh. 6 - Geometry The perimeter of a rectangle is 68 feet...Ch. 6 - Prob. 22RECh. 6 - Prob. 23RECh. 6 - Prob. 24RECh. 6 - Prob. 25RECh. 6 - Prob. 26RECh. 6 - Solving a System by Elimination In Exercises...Ch. 6 - Solving a System by Elimination In Exercises...Ch. 6 - Matching a System with Its Graph In Exercises...Ch. 6 - Prob. 30RECh. 6 - Prob. 31RECh. 6 - Matching a System with Its Graph In Exercises...Ch. 6 - Finding the Equilibrium Point In Exercises 33 and...Ch. 6 - Prob. 34RECh. 6 - Prob. 35RECh. 6 - Prob. 36RECh. 6 - Prob. 37RECh. 6 - Prob. 38RECh. 6 - Prob. 39RECh. 6 - Prob. 40RECh. 6 - Prob. 41RECh. 6 - Prob. 42RECh. 6 - Prob. 43RECh. 6 - Prob. 44RECh. 6 - Prob. 45RECh. 6 - Prob. 46RECh. 6 - Prob. 47RECh. 6 - Prob. 48RECh. 6 - Agriculture A mixture of 6 gallons of chemical A,...Ch. 6 - Sports The Old Course at St Andrews Links in St...Ch. 6 - Investment An inheritance of $40,000 is divided...Ch. 6 - Investment An amount of $46,000 is divided among...Ch. 6 - Prob. 53RECh. 6 - Prob. 54RECh. 6 - Prob. 55RECh. 6 - Prob. 56RECh. 6 - Prob. 57RECh. 6 - Prob. 58RECh. 6 - Prob. 59RECh. 6 - Prob. 60RECh. 6 - Prob. 61RECh. 6 - Prob. 62RECh. 6 - Prob. 63RECh. 6 - Prob. 64RECh. 6 - Prob. 65RECh. 6 - Prob. 66RECh. 6 - Prob. 67RECh. 6 - Prob. 68RECh. 6 - Prob. 69RECh. 6 - Prob. 70RECh. 6 - Prob. 71RECh. 6 - Prob. 72RECh. 6 - Prob. 73RECh. 6 - Prob. 74RECh. 6 - Prob. 75RECh. 6 - Prob. 76RECh. 6 - Prob. 77RECh. 6 - Prob. 78RECh. 6 - Prob. 79RECh. 6 - Prob. 80RECh. 6 - Geometry Write a system of inequalities to...Ch. 6 - Prob. 82RECh. 6 - Consumer Surplus and Producer Surplus In Exercises...Ch. 6 - Consumer Surplus and Producer Surplus In Exercises...Ch. 6 - Inventory Costs A warehouse operator has 24,000...Ch. 6 - Prob. 86RECh. 6 - Prob. 87RECh. 6 - Prob. 88RECh. 6 - Prob. 89RECh. 6 - Prob. 90RECh. 6 - Prob. 91RECh. 6 - Optimal Profit A manufacturer produces two models...Ch. 6 - Prob. 93RECh. 6 - Prob. 94RECh. 6 - Prob. 95RECh. 6 - Prob. 96RECh. 6 - Prob. 97RECh. 6 - Prob. 98RECh. 6 - Prob. 99RECh. 6 - Prob. 100RECh. 6 - Prob. 101RECh. 6 - Prob. 102RECh. 6 - Prob. 103RECh. 6 - Prob. 104RECh. 6 - In Exercises 1-3, solve the system of equations by...Ch. 6 - In Exercises 1-3, solve the system of equations by...Ch. 6 - Prob. 4TCh. 6 - In Exercises 4-6, solve the system of equations...Ch. 6 - Prob. 6TCh. 6 - In Exercises 7 and 8, solve the system of...Ch. 6 - Prob. 8TCh. 6 - In Exercises 9 and 10, solve the system of linear...Ch. 6 - 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- Use your schools library, the Internet, or some other reference source to find the real-life applications of constrained optimization.arrow_forwardA) graph the system of inequalities representing the contraints b)find the value of the objetive function at each corner of the graphed region c)use the values in part b to determine the maximum value of the objetive function and the values of x and y at which the maximum occursarrow_forwardFind the minimum and maximum values of the objective function, and the points at which these values occur subject to the given constraints. Objective Function Constraints f(x, y) = 2x + 4y x ≥ 0 y ≥ 0 x + y ≤ 6arrow_forward
- Maximize the objective function 4x + 4y subject to the following constraints. x+2y = 28 3x +2y = 36 x≤6 x= 0, y = 0 The maximum value of the function is (Simplify your answer.) The value of x is (Simplify your answer.) The value of y is. (Simplify your answer.)arrow_forwardRead the information below and construct the objective function, and the associated constraint inequalities. DO NOT SOLVE THE MINIMUM PROBLEM. A nutritionist advises an individual who is suffering from iron and vitamin-B deficiency to take at least 1700 milligrams (mg) of iron, at least 2300 mg of vitamin B1 (thiamine), and at least 2000 mg of vitamin B2 (riboflavin) over a period of time. Two vitamin pills, brand A and brand B, are suitable to meet these requirements. Each brand A pill costs $0.07 and contains 80 mg of iron, 60 mg of vitamin B1, and 20 mg of vitamin B2. Each brand B pill costs $0.10 and contains 35 mg of iron, 40 mg of vitamins B1, and 28 mg of vitamin B2. Construct the objective function for minimizing the cost, and construct the associated constraint inequalities by selecting the appropriate symbol or number from the dropdown lists below. Note: The symbol = in the dropdown list indicates "greater than or equal to". C [Select] [Select] 60A+ [Select ] [Select] A…arrow_forwardWrite a resource constraint for this situation: A lawn service company has 40 hours of worker time available. Mowing a lawn (x) takes three hours and trimming (y) takes two hours. The profit from mowing is $15 and the profit from trimming is $10.arrow_forward
- Find the absolute maximum and minimum values of the function, subject to the given constraints. 2 2 k(x,y)= -x -y +6x+6y; 0≤x≤ 4, y ≥0, and x+y≤8 The minimum value of k is 1. (Simplify your answer.) The maximum value of k is (Simplify your answer.)arrow_forwardSubject: Math Topic: Linear Programming Instruction: Use a Table for the Data given, Construct the Objective and Constraints Functions, and find the Solution set and Maximize the Sales, and at the end create a graph 1. A Computer Hardware Company produces 2 kinds of CPU Processors : Processor A and Processor B. It takes 2 hours with a cost of P 1500 to manufacture Processor A , while it takes 3 hours with a cost of P 2800 to manufacture Processor B. The Company’s machine can only Operate 345 hours per month and the Company’s Monthly Production Costs Limit is P 300,000 only. Processor A can be sold for P 4500 and Processor B can be sold at P 6500. What is the number of Processor A and Processor B the Company must produce to maximize sales?arrow_forwardThe supplies, demands, and transportation costs per unit are shown on the network. (a)Develop a linear programming model for this problem; be sure to define the variables in your model. Let x11 = amount shipped from Jefferson City to Des Moines x12 = amount shipped from Jefferson City to Kansas City x13 = amount shipped from Jefferson City to St. Louis x21 = amount shipped from Omaha to Des Moines x22 = amount shipped from Omaha to Kansas City x23 = amount shipped from Omaha to St. Louis Min ???????? s.t. From Jefferson City ?????? From Omaha ??????? To Des Moines ??????? To Kansas City ???????? To St. Louis ???????????? x11, x12, x13, x21, x22, x23 ≥ 0 (b)Solve the linear program to determine the optimal solution. Amount Cost Jefferson City–Des Moines Jefferson City–Kansas City Jefferson City–St. Louis Omaha–Des Moines Omaha–Kansas City Omaha–St. Louis Totalarrow_forward
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