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 companys 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 involve in material 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 Ltd a quantity discount of $0.24 a unit on the current price of $24, for all orders of 400 or more units.

a.explain how uncertainties in materials usage and lead time may be incorporated into the analysis.