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 2 labor union(s), to obtain a maximum of $ 14 in donations. (Simplify your answers.)
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Programming
Optimization
Inequalities
Algebra
Formulas
Objective function: z = 150x1 + 200x2
Constraint 1 (Letter writing): 2x1 + 2x2 ≤ 16
Constraint 2 (Follow-up): 1x1 + 3x2 ≤ 14
Theorems
Simplex Method (for optimization)
Feasibility and Boundedness in Linear Programming
Suitable Grade Level
Grades 10-12
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