Math Problem Statement
Solution
To solve the problem, we need to create a linear programming model based on the information provided.
Decision Variables
- Let represent the number of Count Dracula Salamis produced.
- Let represent the number of Frankenstein Sausages produced.
Objective Function
Maximize profit:
Constraints
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Pork availability: (Count Dracula uses 1 pound of pork, and Frankenstein uses 2 pounds per unit.)
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Beef availability: (Count Dracula uses 3 pounds of beef, and Frankenstein uses 2 pounds per unit.)
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Minimum Count Dracula production: At least one-third of the total production should be Count Dracula: Simplify:
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Non-negativity:
Solving the System
I will calculate the optimal solution to maximize the profit under these constraints.
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Math Problem Analysis
Mathematical Concepts
Linear Programming
Optimization
Inequalities
Formulas
Profit = 5y + x
Pork constraint: x + 2y ≤ 1000
Beef constraint: 3x + 2y ≤ 2400
Minimum production constraint: 2x ≥ y
Non-negativity: x ≥ 0, y ≥ 0
Theorems
Feasible Region Theorem
Optimality of Linear Objective Functions
Suitable Grade Level
Grades 11-12 or College Level
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