
Linear Programming Skills Assessment
Authored by Jemal Aman
Others
12th Grade
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5 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Formulate a linear inequality for the following scenario: A company produces two products, X and Y. The profit per unit of X is $10 and the profit per unit of Y is $15. The company can produce at most 100 units of X and 150 units of Y. What is the inequality representing the total profit?
10x + 15y >= P
10x + 15y = P
10x + 15y <= P
10x - 15y <= P
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Identify the feasible region for the following system of inequalities: 2x + 3y ≤ 120, x + y ≤ 60, x ≥ 0, y ≥ 0.
Feasible region is a parabola opening downwards.
Feasible region is the triangle bounded by the lines x=0, y=0, and 2x + 3y = 120.
Feasible region is a rectangle with sides parallel to the axes.
Feasible region is a circle with center at (30, 30) and radius 30.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Solve the following linear programming problem: Maximize Z = 5x + 3y subject to the constraints 2x + y ≤ 10, x + 3y ≤ 12, x ≥ 0, y ≥ 0.
The maximum value of Z is 26.
The maximum value of Z is 15.
The maximum value of Z is 20.
The maximum value of Z is 30.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Interpret the optimal solution in the context of the problem: A farmer has 40 acres of land to plant wheat and barley. Each acre of wheat requires 2 hours of labor and $20 of investment, while each acre of barley requires 3 hours of labor and $30 of investment. If the farmer can afford 120 hours of labor and $800 of investment, and the profit per acre of wheat is $100 and barley is $150, what is the optimal mix of crops?
wheat: 30, barley: 10
{"wheat": 20, "barley": 20}
wheat: 15, barley: 25
wheat: 25, barley: 15
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Apply the simplex method to solve the following linear programming problem: Maximize Z = 3x + 2y subject to the constraints x + y ≤ 4, 2x + y ≤ 5, x ≥ 0, y ≥ 0.
Z = 9, x = 4, y = 1
Z = 7, x = 3, y = 1
Z = 11, x = 2, y = 2
Z = 5, x = 1, y = 2
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