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College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.8: Linear Programming

Problem 31E

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If you are performing a break-even analysis for a business and their cost and revenue equations are dependent, explain what this means for the company's profit margins.
Making furniture Two woodworkers, Chase and Devin, get 100 for making a table and 80 for making a chair. On average, Chase must work 3 hours and Devin 2 hours to make a chair. Chase must work 2 hours and Devin 6 hours to make a table. If neither wishes to work more than 42 hours per week, how many tables and how many chairs should they make each week to maximize their income? Find the maximum income. Table Chair Time Available Devins Time hr 6 2 42 Chases Time hr 2 3 42 Income 100 80
In Example 3, if the accountant earns a profit of 100 on each individual return and a profit of 175 on each business return, find the maximum profit. An accountant prepares tax returns for individuals and for small businesses. On average, each individual return requires 3 hours of her time and 1 hour of computer time. Each business return requires 4 hours of her time and 2 hours of computer time. Because of other business considerations, her time is limited to 240 hours, and the computer time is limited to 100 hours. If she earns a profit of 80 on each individual return and a profit of 150 on each business return, how many returns of each type should she prepare to maximize her profit?
Mathematical Models In Exercises 9 and 10, (a) plot the actual data and the model of the same graph and (b) describe how closely the model represents the data. If the model does not closely represent the data, suggest another type of model that may be a better fit. The ordered pairs below give the revenues y (in billions of dollars) for Activision Blizzard, Inc., from 2008 through 2014. 2008,3.032012,4.862009,4.282013,4.582010,4.452014,4.412011,4.76 A model for the data is y=0.184t+2.32,8t14, where t represents the year, with t=8 corresponding to 2008.
Grandpa and Grandma are treating their family to the movies. Matinee tickets cost $4 per child and $4 per adult. Evening tickets cost $6 per child and $8 per adult. They plan on spending no more than $80 on the matinee tickets and no more than $100 on the evening tickets. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Could they take 9 children and 4 adults to both shows? (d) Could they take 8 children and 5 adults to both shows?
Mary needs to purchase supplies of answer sheets and pencils for a standardized test to be given to the juniors at her high school. The number of the answer sheets needed is at least 5 more than the number of pencils. The pencils cost $2 and the answer sheets cost $1. Mary’s budget for these supplies allows for a maximum cost of $400. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Could Mary purchase 100 pencils and 100 answer sheets? (d) Could Mary purchase 150 pencils and 150 answer sheets?
Philip’s doctor tells him he should add at least 1,000 more calories per day to his usual diet. Philip wants to buy protein bars that cost $1.80 each and have 140 calories and juice that costs $1.25 per bottle and have 125 calories. He doesn’t want to spend more than $12. (a) Write a system of inequalities that models this situation. (b) Graph the system. (c) Can he buy 3 protein bars and 5 bottles of juice? (d) Can he buy 5 protein bars and 3 bottles of juice?
Mary needs to purchase supplies of answer sheets and pencils for a standardized test to be given to the juniors at her high school. The number of the answer sheets needed is at least 5 more than twice the number of pencils. The pencils cost $2 and the answer sheets cost $1. Mary’s budget for these supplies allows for a maximum cost of $400. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Could Mary purchase 100 pencils and 100 answer sheets? (d) Could Mary purchase 150 pencils and 150 answer sheets?
A trailer can carry a maximum weight of 160 pounds and a maximum volume of 15 cubic feet. A microwave oven weighs 30 pounds and has 2 cubic feet of volume, while a printer weighs 20 pounds and has 3 cubic feet of space. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Could 4 microwaves and 2 printers be carried on this trailer? (d) Could 7 microwaves and 3 printers be carried on this trailer?
Give the importance, difference and relationship of Linear Programming and Integer Programming. Site an example or discuss the effect of integer programming in decision making

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Examples of how linear programming can help managers make better decisions Give detailed examples and numbers to back up your points.