Mr Vinny is a wholesaler who buys and sells a wide range of products, one of which is item D. Mr Vinny sell 24000 units of item D each year at a unit price of R20. sales of item D normally follow an even pattern throughout the year. further supplies of item D are ordered whenever the stock falls to this minimum level and the time lag between ordering and delivering is small enough to be ignored.

at present, Mr Vinny buys all his supplies of item D's from Marco Ltd, and usually purchase them in batches of 5000 units. his most recent invoice from Marco Ltd was as follows:

R

basic price: 5000 item Ds at R15 per unit 75000

Delivery charge: transport at R0.50 per unit 2500

fixed shipment per order 1000

78500

in addition, Mr Vinny estimates that each order he places costs him R500, comprising administrative costs and the cost of sample checks. this cost does not vary with the size of the order.

Mr Vinny estimates that the holding costs amount to R18 per item D per annum.

Mr Vinny has recently learnt that another supplier of item Ds, Raymond Ltd, is willing, unlike Marco Ltd, to offer discounts on large orders. Raymond Ltd sells item Ds at the following prices:

order size price per unit (R)

1-2999 15.25

3000-4999 14.50

5000 and over 14.25

in other respects (i.e. delivery charges and the time between ordering and delivery)Raymond Ltd's terms are identical to those of Marco Ltd.

Required:

(a) calculate the optimal re-order quantity for item Ds and the associated annual profit Mr Vinny can expect from their purchase and sale, assuming that he continues to buy from Marco Ltd.

(b) Prepare calculations to show whether Mr Vinny should buy item Ds from Raymond Ltd rather than from Marco Ltd and, if so, in what batch size.

ignoring taxation.