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

Annual demand for a component is 3,600 units, ordering cost is Rs 100 per order and carrying cost is Rs 2 per unit per year. Using calculus on total annual cost T(Q) = (3,600/Q)(100) + (Q/2)(2), the cost-minimising order quantity Q and minimum total cost are:

Total cost is 360,000 divided by Q plus Q. Differentiating and equating to zero gives Q squared equal to 360,000, so the order quantity is 600 units. Ordering and carrying costs are each Rs 600, so minimum total cost is Rs 1,200.

  1. AQ = 600, T = Rs 1,200Correct
  2. BQ = 600, T = Rs 600
  3. CQ = 360, T = Rs 1,360
  4. DQ = 300, T = Rs 1,500

Explanation

T = 360,000/Q + Q. dT/dQ = -360,000/Q^2 + 1 = 0 gives Q^2 = 360,000, so Q = 600. T = 360,000/600 + 600 = 600 + 600 = 1,200. At the optimum ordering and carrying costs are equal. Rs 600 shows only one component of cost.

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