CMA Final · Strategic Cost Management · Linear Programming
Kaveri Feeds Ltd minimises cost Z = 6x + 8y (₹) subject to 2x + y ≥ 12, x + 2y ≥ 12, x + y ≥ 9 and x, y ≥ 0. At the optimal solution, what is the surplus in the constraint 2x + y ≥ 12?
The surplus is 3 units. The least-cost corner is x = 6, y = 3 with cost ₹60. There 2x + y equals 15, which exceeds the required minimum of 12 by 3, so that constraint is not binding.
- A0
- B3Correct
- C6
- D15
Explanation
The corner points are (0,12) with Z=96, (3,6) with Z=66, (6,3) with Z=60 and (12,0) with Z=72. The minimum is at (6,3). There 2x+y = 15, so the surplus over 12 is 3. A surplus of 0 would apply only if that constraint were binding, and it is not. The value 15 is the left-hand side, not the surplus.
Did you get it right without looking?
One question tells you little. A timed set on Linear Programming shows your real accuracy, how long you take and where you lose marks.
More Linear Programming questions
- A feed mix must supply at least 10 units of protein and at least 8 units of fibre. Ingredient X costs ₹6 per kg and gives 2 units of protein…
- Bharat Tools maximises Z = 4x + 2y subject to 2x + y ≤ 10, x ≤ 4, y ≤ 8 and x, y ≥ 0. Which statement is correct?
- Kaveri Ltd maximises Z = 5x + 4y subject to 6x + 4y ≤ 24 and x + 2y ≤ 6, x, y ≥ 0. What is the optimal value of Z?
- A Pune furniture firm's optimal LP plan makes 20 chairs (A) and 15 tables (B). The carpentry-hours constraint is 3A + 2B ≤ 100. How many car…
- A hostel mess in Pune wants to minimise the cost Z = 3x + 4y (Rs) of a mix of two foods. The nutrient constraints are x + y ≥ 10 and x + 3y …
- Sundaram Foods maximises Z = 3x + 2y subject to x + y ≤ 4, x + 3y ≤ 6, x ≤ 3, x, y ≥ 0. Using the optimal solution, which statement is corre…