Linear Programming

16 solved questions from Class 12 Mathematics, each with the full working. Tap any question to see the step-by-step solution.

• 1 What is the domain, range, or fundamental theorem introduced in 'Linear Programming' (Class 12 Mathematics)? medium MCQ Functions & Theorems
• 2 What is the derivative or integral formula associated with 'Linear Programming'? medium MCQ Calculus & Formulae
• 3 How do you find the solution set or optimum value in 'Linear Programming'? medium MCQ Problem Solving & Optimization
• 4 A firm produces product A and product B. 1 unit of A requires 1 unit of resource 1 and 3 units of resource 2. 1 unit of B requires 4 units of resource 1 and 2 units of resource 2. Daily availability: resource 1 = 20 units, resource 2 = 30 units. Profit per unit: A = ₹50, B = ₹60. Using the simplex method, find the maximum profit. medium 3 marks Simplex method for 2‑var LP
• 5 Given the primal LP: minimise Z=3x_1+5x_2 subject to x_1+2x_2ge8 3x_1+x_2le7 x_1,x_2ge0. Find the dual problem, solve the dual using the simplex method, and determine the optimal value of the primal. hard 4 marks Duality and solving dual LP
• 6 A bakery makes cakes and pastries. The profit is ₹40 per cake and ₹30 per pastry. The resources are 2 hours of baking, 4 hours of packaging and 10 units of flour. Each cake needs 0.5 h baking, 0.2 h packaging, 3 units flour. Each pastry needs 0.3 h baking, 0.4 h packaging, 2 units flour. Using the graphical method, what is the maximum profit and how many cakes and pastries should be produced? easy MCQ 2 marks Graphical solution of 2‑variable LP
• 7 Consider the LP: maximise Z=5x_1+8x_2 subject to x_1+2x_2le20 3x_1+x_2le30 x_1,x_2ge0. The optimal solution is x_1=8,;x_2=6. Determine the range of permissible change in the objective coefficient c_1 of x_1 such that the current solution remains optimal. hard 5 marks Sensitivity analysis of objective coefficients
• 8 Minimise Z = 4x_1 + 6x_2 subject to 3x_1 + 5x_2 ≥ 24 2x_1 + x_2 ≥ 10 x_1, x_2 ≥ 0. hard 4 marks Formulating and solving dual via simplex
• 9 Consider the linear programme: maximise Z = 6x + 9y subject to 2x + y ≤ 30, x + 3y ≤ 36, x, y ≥ 0. The optimal solution is x=9, y=4. Find the range of permissible change in the right‑hand side of the first constraint (i.e., in the constant 30) so that the current basis remains optimal. medium 3 marks Sensitivity analysis of RHS
• 10 Which of the following statements about the simplex method is correct? medium MCQ 3 marks Properties of simplex method
• 11 A textile shop manufactures shirts and trousers. The profit per shirt is ₹120 and per trouser is ₹200. The shop has at most 100 meters of fabric and 80 labour hours available per day. Each shirt requires 2 meters of fabric and 1 labour hour, while each trouser requires 4 meters of fabric and 2 labour hours. Using the graphical method, determine the number of shirts and trousers that should be produced each day to maximise profit, and state the maximum profit. easy 2 marks Graphical solution of two‑variable LP
• 12 Maximise (Z=4x_1+5x_2) subject to x_1+2x_2≤ 8 3x_1+x_2≤ 9 x_1,x_2≥ 0. Solve this linear programme using the simplex method and give the optimal values of (x_1,x_2) and (Z). hard 5 marks Simplex algorithm
• 13 A company produces two products X and Y. The profit per unit of X is ₹50 and that of Y is ₹70. The resources available each day are described by the following constraints: 1. 3X + 2Y ≤ 60 2. 2X + 4Y ≤ 48 If X and Y must be non‑negative, determine the production quantities that maximise the total profit and state the maximum profit using the graphical method. medium 2 marks Graphical method for LP
• 14 Maximise (Z=3x+2y) subject to (x+2yle 10), (4x+yle 12), (x,yge 0). Solve this linear programme using the simplex method and give the optimal values of ((x,y)) and (Z). medium 3 marks Simplex method for LP
• 15 A factory produces two kinds of notebooks: A and B. Profit per unit is ₹30 for A and ₹45 for B. The available resources each day are described by: 1. (5A+3Ble 90) (paper) 2. (2A+4Ble 64) (labour) If (A,Bge 0), find the production quantities that maximise the total profit using the graphical method and state the maximum profit. easy 2 marks Graphical solution of 2‑variable LP
• 16 Which of the following statements about the simplex method is correct? easy MCQ 1 mark Correct properties of simplex