CMA Final · Strategic Cost Management · Linear Programming
A cattle-feed unit blends two ingredients P and Q to minimise cost C = 6p + 8q (₹ per batch). Each batch must satisfy protein 2p + q ≥ 10 and fibre p + 2q ≥ 8, with p, q ≥ 0. What is the minimum cost?
The minimum cost is ₹40. The feasible region has corner points (0,10), (4,2) and (8,0) with costs ₹80, ₹40 and ₹48. The blend of 4 units of P and 2 units of Q meets both requirements at lowest cost.
- A₹40Correct
- B₹48
- C₹80
- D₹44
Explanation
The corner points are (0,10), (4,2) and (8,0). The point (4,2) is where 2p + q = 10 and p + 2q = 8 meet. Costs are 80, 24 + 16 = 40 and 48 respectively. The minimum is ₹40. ₹48 comes from using only P and ₹80 from using only Q.
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