Math Problem Statement
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 $150 from each church group and $200 from each union local, and she has a maximum of 16 hours of letter writing and a maximum of 14 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. Question content area bottom Part 1 Let x 1 be the number of church groups, and let x 2 be the number of labor unions. What is the objective function? zequals
150x 1plus
200x 2 (Do not include the $ symbol in your answers.) Part 2 She should contact
enter your response here church group(s) and
enter your response here labor union(s), to obtain a maximum of $
enter your response here in donations.
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Linear Programming
Optimization
Algebra
Formulas
Objective function: z = 150x1 + 200x2
Constraints: 2x1 + 2x2 ≤ 16 (letter writing), 1x1 + 3x2 ≤ 14 (follow-up time)
Theorems
Linear Programming Theorem
Suitable Grade Level
College Level
Related Recommendation
Maximizing Fundraising with Linear Programming for Donna De Paul
Linear Programming: Maximize Donna's Fundraising Efforts with Church Groups and Labor Unions
Maximizing Donations with Linear Programming: Church Groups vs Labor Unions
Maximizing Donations Using Linear Programming: Church Groups and Labor Unions
Maximizing Fundraising Using Linear Programming: Church Groups and Labor Unions