Demand for microwave ovens is steady, averaging N per year. A retail merchant buys them at a basic cost of P each, the cost of storing each unit is H per year, and each order made incurs a cost of C. The merchant places orders of size Q, and re-orders just before stock runs out. (a) Explain why the average annual cost associated with this policy is NP + HQ/2 + CN/Q. (1) and find the value of Q that minimises this cost. (b) Consider the expression (1) from part (a) with N = 5000, P = 20, H = 4 and C = 100. i. What size of order will minimise the cost? ii. The supplier offers discounts on the basic cost Pif the order is sufficiently large: the discount is 1% on orders of at least 200, 1.5% if it is at least 400, 2.5% for orders of 1000 or more, and 3% on orders of at least 1500. State, with reasons, which are the only three order sizes you need examine in detail to identify the minimum cost. iii. Find the cheapest order size for the situation described in part (ii).