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College Algebra (MindTap Course List)

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 28E: Production A small country exports soybeans and flowers. Soybeans require 8 workers per acre,...

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A farmer is going to divide her 40 acre farm between two crops. Seed for crop A costs $25 per acre. Seed for crop B costs $50 per acre. The farmer can spend at most $1250 on seed.

If crop B brings in a profit of $310 per acre, and crop A brings in a profit of $130 per acre, how many acres of each crop should the farmer plant to maximize her profit?

acres of crop A
acres of crop B

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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
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?
Production A small country exports soybeans and flowers. Soybeans require 8 workers per acre, flowers require 12 workers per acre, and 100, 000 workers are available. Government contracts require that there be at least 3 times as many acres of soybeans as flowers planted. It costs 250 per acre to plant soybeans and 300 per acre to plant flowers, and there is a budget of 3 million. If the profit from soybeans is 1600 per acre and the profit from flowers is 2000 per acre, how many acres of each crop should be planted to maximize profit? Find the maximum profit.

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