Donna De Paul is raising money for the homeless. She discovers that each church group requires 2 hours of letter writing and 1 hour of follow-up, while for each labor union she needs 2 hours ofletter writing and 3 hours of follow-up. Donna can raise $125 from each church group and $200 from each union local, and she has a maximum of 20 hours of letter writing and a maximum of 12hours of follow-up available per month. Determine the most profitable mixture of groups she should contact and the most money she can raise in a month.Let x, be the number of church groups, and let x, be the number of labor unions. What is the objective function?z= x, + x2(Do not include the $ symbol in your answers.)

Answered: raising money for the homeless. She…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 8T

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Donna De Paul is raising money for the homeless. She discovers that each church group requires 2 hours of letter writing and 1 hour of follow-up, while for each labor union she needs 2 hours of
letter writing and 3 hours of follow-up. Donna can raise $125 from each church group and $200 from each union local, and she has a maximum of 20 hours of letter writing and a maximum of 12
hours of follow-up available per month. Determine the most profitable mixture of groups she should contact and the most money she can raise in a month.
Let x, be the number of church groups, and let x, be the number of labor unions. What is the objective function?
z= x, + x2
(Do not include the $ symbol in your answers.)

Expert Solution

Step 1

In the given question, the concept of Linear Programming is applied.

Linear Programming

An approach to optimizing operations with restrictions is called linear programming. Linear programming's basic goal is to maximize or minimize numerical values. It is made up of linear functions that are constrained by inequalities or equations. Linear programming is a useful technique for determining the most efficient use of resources. Linear programming is a term made up of two words: linear and programming. The term "linear" refers to a one-dimensional relationship between two or more variables. The term "programming" refers to the process of choosing the optimal answer out of a number of options.