Linear Programming
Himachal Pradesh Board · Class 12 · Mathematics
Practice quiz for Linear Programming — Himachal Pradesh Board Class 12 Mathematics. MCQs and questions with answers to test your preparation.
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A company produces chairs and tables. Each chair requires 2 hours of labor and each table requires 3 hours. If the company has 120 hours of labor available, which inequality represents this constraint if x is chairs and y is tables?
The optimal solution of a linear programming problem occurs at which type of point in the feasible region?
A manufacturer produces two products A and B. Product A requires 2 hours of labor and Product B requires 3 hours. If the manufacturer has 120 hours of labor available and wants to maximize profit where profit from A is Rs 40 and from B is Rs 60, which constraint represents the labor limitation if x and y are quantities of A and B respectively?
If the objective function Z = 5x + 3y has values Z = 15 at (3, 0), Z = 21 at (3, 2), and Z = 18 at (0, 6), what is the maximum value of Z?
Sample Questions
Find the corner points of the feasible region defined by: x + y ≤ 6, 2x + y ≤ 8, x ≥ 0, y ≥ 0
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(0, 0), (0, 6), (4, 0), (2, 4)
Corner points are intersections of constraint boundaries. Step 1: Origin (0,0). Step 2: x=0, x+y=6 gives (0,6). Step 3: y=0, 2x+y=8 gives (4,0). Step 4: Solve x+y=6 and 2x+y=8 simultaneously: x=2, y=4, giving (2,4). Verify all points satisfy all constraints.
If the objective function is Z = 3x + 4y and the corner points are (0,0), (0,5), (4,0), and (2,3), what is the maximum value of Z?
A linear programming problem always has a unique optimal solution.
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False
This statement is false. A linear programming problem can have: Step 1: Unique optimal solution (one corner point gives optimum). Step 2: Multiple optimal solutions (objective function parallel to a constraint). Step 3: No solution (infeasible region). Step 4: Unbounded solution (feasible region extends infinitely in direction of optimization).
A bakery makes cakes and pastries. Profit per cake is ₹50 and per pastry is ₹30. If x = cakes and y = pastries, write the objective function to maximize profit.
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