Grade 12 Linear Programming Worksheet
This worksheet covers key concepts in linear programming, including formulating objective functions, constraints, and identifying feasible regions.
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Grade 12 Linear Programming Worksheet
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Read each question carefully and provide clear, concise answers. Show all your work for problems requiring calculations or graphing.
1. In linear programming, the function to be maximized or minimized is called the function.
2. The conditions that limit the variables in a linear programming problem are known as .
3. The set of all possible solutions that satisfy all constraints is called the region.
1. Which of the following is NOT a characteristic of a linear programming problem?
Objective function is linear
Constraints are linear inequalities
Non-negativity restrictions on variables
Constraints are non-linear equations
2. The optimal solution to a linear programming problem always occurs at a/an:
Interior point of the feasible region
Edge of the feasible region
Vertex of the feasible region
Outside the feasible region
1. A company manufactures two types of products, A and B. Product A requires 2 hours of labor and 1 unit of raw material. Product B requires 1 hour of labor and 2 units of raw material. The company has 100 hours of labor and 80 units of raw material available. Let x be the number of units of Product A and y be the number of units of Product B. Formulate the constraints for this problem.
Consider the following linear programming problem:
Maximize P = 5x + 3y
Subject to:
x + y ≤ 7
2x + y ≤ 10
x ≥ 0, y ≥ 0
1. Graph the feasible region for the given constraints.
2. Identify the vertices of the feasible region.
3. Evaluate the objective function P = 5x + 3y at each vertex to find the maximum value.