Wagtail Ltd uses the 'optimal batch size' model (see below) to determine optimal levels of raw materials. Material B is consumed at a steady, known rate over the company's planning horizon of one year; the current usage is 4000 units per annum. The costs of ordering B are invariant with respect to order size; clerical costs of ordering have been calculated at £30 per order. Each order is checked by an employee engaged in using B in production who earns £8 per hour irrespective of his output. The employee generates a contribution of £1 per hour when not involved in materials checks and the stock check takes five hours. Holding costs amount to £15 per unit per annum.
The supplier of material B has very recently offered Wagtail a quantity discount of £0.24 a unit on the current price of £24, for all orders of 400 or more units of B.
(a) Calculate the optimal order level of material B, ignoring the quantity discount;
(b) Evaluate whether the quantity discount offered should be taken up by Wagtail;