Linear Programming

Formulation, graphical method for two-variable LP problems, feasible region, optimal solution.

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Q1 · Linear Programming · EASY
A furniture manufacturer produces chairs and tables. Each chair requires 3 hours of carpentry work and each table requires 5 hours of carpentry work. The manufacturer has 60 hours of carpentry time available per week. If x represents the number of chairs and y represents the number of tables, which inequality correctly represents this constraint?
Q2 · Linear Programming · MEDIUM
A company manufactures two products P and Q. The profit per unit of P is Rs. 40 and per unit of Q is Rs. 30. The constraints are: x + 2y ≤ 10 and 3x + y ≤ 15, where x and y are the number of units of P and Q respectively. Also, x ≥ 0 and y ≥ 0. What is the maximum profit?
Q3 · Linear Programming · MEDIUM
The feasible region for a linear programming problem is shown by the inequalities: x + y ≤ 4, 2x + y ≤ 6, x ≥ 0, y ≥ 0. The objective is to minimize Z = 6x + 4y. At which corner point does the minimum value occur?
Q4 · Linear Programming · HARD
A manufacturer produces two types of products A and B. Each unit of A requires 2 kg of raw material and 4 hours of labour. Each unit of B requires 3 kg of raw material and 2 hours of labour. The manufacturer has 120 kg of raw material and 100 hours of labour available. If the profit on A is Rs. 50 per unit and on B is Rs. 40 per unit, and if x units of A and y units of B are produced to maximize profit, which of the following statements about the optimal solution is correct?
Q5 · Linear Programming · MEDIUM
A feasible region is bounded by the constraints x + 2y ≤ 10, x + y ≤ 6, x ≥ 0, y ≥ 0. If the objective function is Z = 3x + 4y and Z attains its maximum at two corner points (2, 4) and (0, 5), then the ratio of the coefficients is: