J Peterman Catalog Co (JPC) is a major catalog sales company in greater Manhattan. To produce these catalog products, JPC employs the services of one of the largest contract manufacturers, Kramerica Company (KC). JPC is now considering to change the manner in which it interacts with KC. To provide some background, the supply chain for catalog fashion apparel works approximately as follows: Because the lead times for acquiring fabric are very long, all fabric must be procured far in advance of the selling season when demand is still uncertain. By the time that garments are produced, there is much less demand uncertainty, but obviously the amount that can be produced is limited by the amount of fabric that was acquired. To keep things simple, we will assume that all production is make-to- order. That is, we will assume that units can be produced after they are demanded. We will also assume that production capacity is limited only by the availability of fabric. We will consider a garment that JPC sells for $50 per unit. At the time that fabric must be procured, it is known that demand for the garment follows a normal distribution with a mean of 30,000 units and the standard deviation of 10,000. The cost of fabric is $15 per unit and the KC's additional cost of delivering a completed garment, e.g. cutting, sewing, packaging, shipping, etc., is $10 per unit. Any fabric that is not needed to satisfy demand can be sold off for $5 per unit. (Assume one unit of fabric is required to make one garment.) The following figure represents the time- Iine of demand and supply: Production 8:. Delivery Fabric Procurement $10 per unit 515 per unit (in addition to fabn'c cost) Sell unused fabric Demand Forecast Demand occurs 55 per unit Under the traditional arrangement, JPC has agreed to pay KC a wholesale price of $30 per unit of the garment that KC delivers in response to demand. Under this arrangement, it was KC's responsibility to acquire the fabric. Because KC had to pay for the fabric, it would also determine the amount to procure. A) Under the traditional arrangement, how many units of fabric should KC procure in order to maximize its prots