IEOR 3402: Assignment 3 Problems

IEOR 3402: Assignment 3• Hand in solutions to the starred problems only.• You may work individually, or as a group of 2 students. (If you work as a group, pleasesubmit one assignment per group.)1. Nahmias, 3.7.2. Nahmias, 3.12.3. Nahmias, 3.32.4. * Nahmias, 3.34. Assume that you must satisfy all demands without back-orders or lostsales. You may use EXCEL or any other LP solver.5. * In class, we have formulated the following linear program:max XTt=1r · St + h · Its. t. St ? dt ?t = 1, . . . , TXt ? Ct ?t = 1, . . . , TIt ? It?1 + Xt ? St ?t = 2, . . . , TI0 = 0It, St, Xt ? 0 ?t = 1, . . . , T.One of the underlying assumptions of this model was the any excess demand that cannotbe satisfied immediately will be lost (lost sales). Suppose instead that any excess demandthat cannot be satisfied immediately will be carried over to the next period (backlogging),and any backordered unit will incur the cost of $b per period. Develop a linear program forthis problem by modifying the above formulation.6. * You have just been made corporate vice president in charge of manufacturing for anautomotive components company and are directly in charge of assigning products to plants.Among many other products, the firm makes automotive batteries in three grades: heavyduty,standard, and economy. The unit net profits and maximum daily demands for theseproducts are given in the first table below. The firm has three locations where the batteriescan be produced. The maximum assembly capacities, for any mix of battery grades, aregiven in the second table below. The number of batteries that can be produced at a locationis also limited by the amount of suitably formulated lead the location can produce. The leadrequirements for each grade of battery and the maximum lead production for each locationare also given in the following tables.Unit Profit Max Demand Lead RequirementProduct ($/battery) (batteries/day) (lbs/battery)Heavy-duty 12 700 21Standard 10 900 17Economy 7 450 141Plant Assembly Capacity Maximum Lead ProductionLocation (batteries/day) (lbs/day)1 550 10,0002 750 7,0003 225 4,200(a) Formulate a linear program that allocates production of the three grades among thethree locations in a manner that maximizes profit.(b) Suppose company policy requires that the fraction of capacity (units scheduled/assemblycapacity) be the same at all locations. Show how to modify your LP to incorporatethis constraint.(c) Suppose company policy dictates that at least 50 percent of the batteries producedmust be heavy-duty. Show how to modify your LP to incorporate this constraint.