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CMA Final · Strategic Cost Management · Business Application of Maxima and Minima

Sagar Plastics has annual demand of 1,600 units, ordering cost of Rs 400 per order and carrying cost of Rs 8 per unit per year. Treating total cost T(Q) = (1,600/Q)*400 + (Q/2)*8 and minimising it by calculus, the optimum order quantity Q and the minimum total of ordering plus carrying cost are:

The optimum order quantity is 400 units with a minimum cost of Rs 3,200. Differentiating 640,000/Q + 4Q and equating to zero gives Q squared of 160,000; at 400 units ordering and carrying costs are Rs 1,600 each.

  1. AQ = 400; cost Rs 3,200Correct
  2. BQ = 400; cost Rs 1,600
  3. CQ = 800; cost Rs 3,200
  4. DQ = 200; cost Rs 3,200

Explanation

T = 640,000/Q + 4Q. dT/dQ = -640,000/Q^2 + 4 = 0 gives Q^2 = 160,000, so Q = 400. T = 1,600 + 1,600 = Rs 3,200. Rs 1,600 is only one component (ordering or carrying), a partial cost.

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