Math Problem Statement
et up the following linear programming problem. The variables have already been defined for you. Be sure to indicate whether the objective function is being maximized or minimized. You may not need all of the blanks provided for the constraints. Ruby has a hard time being productive on the weekends, so she likes to pretend she’s on a game show called “You. Better. Work!” On this imagined game show, she earns 100 points for each homework assignment she completes and 50 points for each household chore she completes. This weekend, Ruby has at most 8 hours with which to complete tasks. She estimates that each homework assignment will take 1 hour to complete, and each household chore will take 45 minutes to complete. However, she has no more than 5 homework assignments that she needs to complete this weekend. How many of each task should Ruby complete in order to earn the most points possible? Variables: h := the number of homework assignments completed c := the number of household chores completed P := the number of points earned while playing “You. Better. Work!” Objective: Maximize / Minimize Subject to: 1
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Programming
Optimization
Inequalities
Formulas
Objective Function: P = 100h + 50c
Time Constraint: 60h + 45c ≤ 480 (or simplified 4h + 3c ≤ 32)
Homework Constraint: h ≤ 5
Non-negativity Constraints: h ≥ 0, c ≥ 0
Theorems
Linear Programming Feasibility Theorem
Suitable Grade Level
Grades 10-12
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