Linear Programming Worksheet
A Grade 11 math worksheet covering linear programming concepts, including graphing inequalities, identifying feasible regions, and optimizing objective functions.
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Linear Programming Worksheet
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Read each question carefully and show all your work. Use the provided graph paper for graphing exercises.
1. Graph the following system of inequalities on the coordinate plane below and shade the feasible region:
a) x + y ≤ 6
b) 2x - y ≥ 0
c) x ≥ 0, y ≥ 0
2. Complete the following sentences with the correct linear programming term:
a) The region that satisfies all constraints in a linear programming problem is called the region.
b) A function is an expression that needs to be maximized or minimized.
c) The inequalities that define the boundaries of the feasible region are known as .
3. Which of the following is NOT a characteristic of a linear programming problem?
Linear objective function
Non-linear constraints
Non-negativity constraints
Feasible region
4. Consider the following linear programming problem:
Maximize P = 3x + 2y
Subject to:
x + y ≤ 5
x ≥ 0, y ≥ 0
a) Graph the feasible region for this problem.
b) Identify the coordinates of the corner points of the feasible region.
c) Determine the maximum value of P.
5. State whether each statement is True or False:
a) The optimal solution to a linear programming problem always occurs at a corner point of the feasible region.
True
False
b) A feasible region must be bounded to have an optimal solution.
True
False