Mr. Marley is a wholesaler who buys and sells a wide range of products, one of which is the Laker. Mr. Marley sells 24,000 units of the Laker each year at a unit price $20. Sales of the Laker normally follow an even pattern throughout the year but to protect himself against possible deviations Mr. Marley keeps a minimum stock of 1,000 units. Further supplies of the Laker are ordered whenever the stock falls to this minimum level and the time lag between ordering and delivery is small enough to be ignored.
At present, Mr Marley buys all his supplies of Lakers from May Ltd and usually purchases in batches of 5,000 units. His most recent invoice from May Ltd was as follows:
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$
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Basic price: 5,000 Lakers @ $15 per unit
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75,000
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Delivery charge: Transport at $0.50 per unit
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2,500
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Fixed shipment charge per order
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1,000
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TOTAL
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78,500
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In addition, Mr. Marley estimates that each order he places costs him $500, comprising administrative costs and the cost of sample checks. This cost does not vary with the size of the order.
Mr. Marley stores Lakers in a warehouse which he rents on a long lease for $5 per square foot per annum. Warehouse space available exceeds current requirements and, as the lease cannot be cancelled, spare capacity is sublet on annual contracts at$4 per square foot per annum. Each unit of Laker in stock requires two square feet of space. Mr. Marley estimates that other holding costs amount to $10 per Laker per annum.
Mr. Marley has recently learnt that another supplier of Lakers , Richardson Ltd, is willing, unlike May Ltd, to offer discounts on large orders. Richardson Ltd sells Lakers at the following prices:
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Order Size
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Price per unit ($)
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1 - 2,999
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15.25
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3,000 - 4,999
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14.50
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5,000 and over
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14.25
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In other respects (i.e. delivery charges and the time between ordering and delivery) Richardson Ltd's terms are identical to those of May Ltd. You are required to:
a. Calculate the optimal re-order quantity for Lakers and the associated annual profit Mr. Marley can expect from their purchase and sale, assuming that he continues to buy from May Ltd.
b. Prepare calculation to show whether Mr. Marley should buy Lakers from Richardson Ltd rather than from May Ltd and, if so, in what batch sizes.
c. Explain the limitations of the methods of analysis you have used.