CMA Final · Strategic Cost Management · Business Application of Maxima and Minima
A company must order a yearly requirement of 7,200 units. Ordering cost is Rs 250 per order and carrying cost is Rs 10 per unit per year. Treating total relevant cost T(Q) = 7200/Q × 250 + 10Q/2 as a function of order size Q, what is the minimum total relevant cost?
The minimum total relevant cost is Rs 6,000 at an order size of 600 units.
- ARs 15,000
- BRs 18,000Correct
- CRs 20,000
- DRs 24,000
Explanation
T = 1,800,000/Q + 5Q. dT/dQ = -1,800,000/Q² + 5 = 0 gives Q² = 360,000, Q = 600. T = 3,000 + 3,000 = 6,000. Checking: 12 orders × 250 = 3,000 and average stock 300 × 10 = 3,000. The minimum is Rs 6,000, so the options need revision.
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