For problems, show your calculations in detail. For qualitative questions, explain your answer and reasoning clearly. You may refer to the course book or the class notes. You may work in groups with your classmates, but each of you must type/write your own assignment submission. 1. Consider an item with a demand rate (D) of 200 units per year and a unit cost (v) of $30. If the fixed cost of ordering (A) is $75 and the carrying charge (i) is 25 percent, and the Lead Time (L) is zero (i.e., the order is delivered instantaneously). Answer each part independently. a. Determine the optimal order quantity (EOQ), the cycle length (in terms of days), and the average cycle cost (i.e., average annual cost). b. Determine when to order within each cycle (i.e., the reorder point) if the Lead Time (L) increases to 30 days. c. If the actual order quantity is 10% higher than the EOQ, how much will the average cycle cost increase (over the average cycle cost for EOQ, computed in (a))? d. The purchasing manager wants to know how low the fixed cost of ordering cost should be for the EOQ to be equal to 1 unit. e. Constrained EOQ: For each of the following cases, determine the optimal order quantity if each order needs to be no less than Qmin units and no more than Qmax units. Hint: See the shape of the Total Cost curve, and remember that the unconstrained EOQ (from (a)) corresponds to the minimum point of this curve. When there are restrictions on order quantity, the EOQ from (a) may no longer be feasible, and may need to be modified so it is feasible, i.e., within [Qmin, Qmax]. 1. Qmin=30 and Qmax=50 2. Qmin=30 and Qmax=80 3. Qmin=80 and Qmax=100 2. A manufacturing firm uses a three-month supply rule to determine the production quantity. The following data is given: D = 2,000 units/year A = $5 per production v = 4 per 100 units r = 20% a. Determine the EOQ. b. The production manager is not convinced that the estimate for A reflects the true setup cost (aka the fixed cost of ordering). What should be the value for A so that the EOQ equals the three-month supply rule? Explain.