A student earns $10 per hour for tutoring and $7 per hour as a teacher's aide. To have enough free time for studies, he can work no more than 20 hours per week. The tutoring center requires that each tutor spends at least three hours per week tutoring, but no more than eight hours per week. How many hours should he work to maximize his earnings? hours of tutoring hours as a teacher's aide What is the maximum profit? S Question Help: D Post to forum

A student earns $10 per hour for tutoring and $7 per hour as a teacher's aide. To have enough free time for studies, he can work no more than 20 hours per week. The tutoring center requires that each tutor spends at least three hours per week tutoring, but no more than eight hours per week. How many hours should he work to maximize his earnings? hours of tutoring hours as a teacher's aide What is the maximum profit? S Question Help: D Post to forum

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 3SC: In Example 3, if the accountant earns a profit of 100 on each individual return and a profit of 175...

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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
Making crafts Two artists, Nine and Rob, make yard ornaments. They get 80 for each wooden snowman they make and 64 for each wooden Santa Claus. On average, Nina must work 4 hours and Rob 2 hours to make a snowman. Nina must work 3 hours and Rob 4 hours to make a Santa Claus. If neither wishes to work more than 20 hours per week, how many of each ornament should they make each week to maximize their income? Find the maximum income. Snowman Santa Claus Time Available Robs Time hr 2 4 20 Ninas Time hr 4 3 20 Income 80 64
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?
Use your schools library, the Internet, or some other reference source to find the real-life applications of constrained optimization.