Questions and Answers
What values of x and y maximize the objective function by graphing the system of constraints?
(5, 0)
What values of x and y minimize the objective function for C = x + 3y?
(8, 0)
What values of x and y maximize the objective function for P = 3x + 2y?
(6, 2)
What is the maximum value for P = 2x + y using the values of x and y that maximize the objective function?
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What is the maximum value for P = 3x + 2y using the values of x and y that maximize the objective function?
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What is the minimum value for C = 8x + 5y using the values of x and y that minimize the objective function?
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How many trays of corn muffins and bran muffins should the baker make to maximize profit?
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What is the maximum value for P = x + 2y using the values of x and y that maximize the objective function?
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What is the minimum value for P = 10,000x + 20,000y using the values of x and y that minimize the objective function?
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What is the maximum value for P = 4x + 3y using the values of x and y that maximize the objective function?
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Study Notes
Maximizing and Minimizing Objective Functions
- Optimal values of (x, y) for maximizing objective function found by graphing constraints.
- Maximum for P = 3x + 2y occurs at (6, 2).
- Maximum value for P = 2x + y is P = 6.
- Maximum value for P = x + 2y is P = 400.
- Maximum for P = 4x + 3y results in P = 51.
Minimum Values of Objective Functions
- Values of (x, y) for minimizing objective function are derived through graphing.
- Minimum for C = x + 3y occurs at (8, 0).
- Minimum value for C = 8x + 5y is C = 633 1/3.
- Minimum for C = 10,000x + 20,000y gives P = 67,370.
Muffin Baking Problem
- Process involves constraints related to ingredients in baking.
- Corn muffins require 4 cups of milk and 3 cups of wheat flour.
- Bran muffins require 2 cups of milk and 3 cups of wheat flour.
- Ingredient availability: 16 cups of milk and 15 cups of wheat flour.
- Profit analysis results in producing 3 trays of corn muffins and 2 trays of bran muffins for maximum profit.
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Description
Explore the concepts of linear programming with this flashcard quiz focused on finding optimal solutions through graphing systems of constraints. Master techniques to maximize and minimize objective functions effectively. Test your understanding of variables x and y in various scenarios.
