LPP formulation, graphical method, feasible region, optimal solutions.
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Q1 · Linear Programming (Class 12) · EASY
A manufacturer produces two types of items A and B. Each item of type A requires 2 hours on Machine I and 3 hours on Machine II. Each item of type B requires 3 hours on Machine I and 2 hours on Machine II. Machine I is available for 12 hours and Machine II is available for 12 hours per day. If x and y denote the number of items of type A and B produced per day respectively, which of the following is NOT a constraint in the linear programming formulation?
Q2 · Linear Programming (Class 12) · MEDIUM
The feasible region for a linear programming problem is shown in the coordinate plane with corner points at O(0,0), A(5,0), B(4,3), and C(0,6). If the objective function is Z = 3x + 4y, what is the maximum value of Z?
Q3 · Linear Programming (Class 12) · HARD
A company manufactures two products P and Q. The profit per unit of P is Rs. 50 and that of Q is Rs. 40. Each unit of P requires 2 kg of raw material and 3 hours of labour. Each unit of Q requires 3 kg of raw material and 2 hours of labour. The company has 120 kg of raw material and 100 hours of labour available. If the company wants to maximize profit, how many units of product P should be manufactured?
Q4 · Linear Programming (Class 12) · EASY
The corner points of the feasible region for a linear programming problem are (0,0), (5,0), (3,4), and (0,6). If the objective function is Z = 4x + 5y, the maximum value of Z is: