In this problem, your company is a distributor of products. You serve as an inventory manager for the regional distribution center (DC) here in the Atlanta area. In this role, you schedule the purchase and shipment of products from various suppliers inbound to the Atlanta DC. Once you receive the products at the DC, they are stored in inventory until they are picked, packed, and shipped outbound to your company's downstream customers in response to orders. For each of your products, you currently use a single, dedicated supplier. Each of your suppliers ships their products to you from their facility using trucking services, and they provide you with choices of different LTL or truckload trucking carriers depending on your shipment size. Consider managing inventory now for product 101 produced by Supplier A. Currently, you face demand for product 101 of about 200 units per week. Each unit of product 101 has a purchase cost p of $500 and you decide to value your inventory at the slightly higher rate of $550 (v). As is typical, you are required to pay for products when you order. For inventory carrying cost (either in-transit or at your facility), you assume an annual carrying cost rate r = 18% per year; this rate includes your capital cost but also components that model product quality loss over time, risk of theft, and risk of obsolescence. You estimate that storing one item of product 101 in your DC requires an equivalent rent (storage cost) $10 per unit per year. of s = 2. Suppose you consider shipping full truckloads (q = 700 units) each time you order. How frequently will ship full truckloads? Express your answer by stating how many f truckloads per week (and note that ƒ can be fractional and less than one). Another useful quantity is the headway H between shipments, where H 1. What is the headway H in weeks? = 3. To better visualize both the arrival of shipments to your DC and your pipeline inven- tory, draw two cumulative curves (time in weeks on x-axis, cumulative items on the y-axis). The first curve, Ds(t) should begin at the origin (0,0) and then increase by q every time your supplier sends a shipment (every 7H days). The second curve, Ac(t), should also begin at the origin and only increase when a shipment of size q arrives at your DC facility. Plot both curves accurately for a minimum of 4 shipments. What is the maximum number of units in the pipeline? If there are times when no units remain in the pipeline, what fraction of days is the pipeline inventory zero?