ASSIGNMENT-3 QUANTITATIVE METHODS (STAT-201) Student Full Name: Student ID: CRN No.: Note: 1. All questions are compulsory. 2. Due date: December 12, 2016 11:59 PM. 3. Points: Section-I 16=6 Section-II 16=6 Section-III 63=18 Total 30 Section-I State whether the following statements are True or False. (16 = 6) 1. A transportation model must have the same numbers of rows as columns. 2. We get the optimum solution by North West Corner rule. 3. Using LP to determine the most economical and effective nutritional programme for patients is an application known as the diet problem. 4. In a quantity discount model, the purchase cost or material cost must be included in the total cost calculation. 5. The reorder point is found by adding the average daily demand and the lead time. 6. The overall objective of the quantity discount model is to minimize the total inventory. Section-II Circle/tick the right answer from the answers given below. (16 = 6) 1. In making inventory decisions, the purpose of the basic EOQ model is to (a) Minimize carrying costs. (b) Minimize ordering costs. (c) Minimize the sum of carrying costs and ordering costs. (d) Minimize customer dissatisfaction. 2. The point at which to reorder depends directly on which of the following (a) Lead time (b) EOQ 2 (c) Ordering cost (d) Storage cost 3. When the items are being moved from a source to a destination through an Intermediate point, the problem is called (a) Assignment problem (b) Transportation problem (c) Transshipment problem (d) Inventory control problem 4. An objective function for transportation problem is given (all the notations have their usual meanings) by (a) Cij Xij (b) Xij (c) Xij Si (d) Xij = dj 5. In the transportation problem, if the number of occupied square in any solution is less than the number of row plus number of columns minus 1, then the problem is called (a) balance transportation problem (b) degenerate transportation problem (c) dummy destination problem (d) none of the above 6. When applying LP to diet problems, the objective function is usually designed to (a) Maximize profits from blends of nutrients. (b) Maximize ingredient blends. (c) Minimize production losses. (d) Minimize the costs of nutrient blends. Section-III Answer the following Essay Type Questions (63=18) 1. Lila Battle has determined that the demand for screw is 100,000 screws. Lila who works in her brother's hardware store is in charge of purchasing. She estimate that it costs $10 every time an order is placed. This cost include her wages, the cost of the forms used in placing the order and so on. Furthermore, she estimate that the cost of carrying one screw in inventory for a year is 0.005. Assume that the demand is constant throughout the year. (a) How many screws should Lila order at a time if she wishes to minimize total inventory cost? (b) How many order per year would be placed? (c) What would the annual ordering cost be? 3 (d) What would the average inventory be? (e) What would the annual holding cost be? 2. The Samsung Company carries a variety of electronic inventory items. For the LED TV the daily demand is normally distributed with a mean of 125 units, standard deviation of 30 and lead time is 16 days. Samsung wants to maintain 95% service level. What is the reorder point and how much safety stock should be carried? 3. Fleming Accessories produces paper slicers used in offices and in art stores. The minislicer has been one of its most popular items: Annual demand is 6,750 units and is constant throughout the year. Kristen Fleming owner of the firm, produces the minislicers in batches. On average Fleming can manufacture 125 minislicers per day. Demand for these slicers during the production process is 30 per day. The setup cost for the equipment necessary to produce the minislicers is $150. Carrying cost are $1 per minislicers per year. How many minislicers should Fleming manufacture in each batch? 4. Four warehouse are supplied by four factories. The supply available from each factory, the demand at each warehouse and the cost per unit of transporting goods from the factories to the ware houses are summarized in the following table. Find the initial basic feasible solution. Ware house Factory E F G H Supply A 10 30 25 15 14 B 20 15 20 10 10 C 10 30 20 20 15 D 30 40 35 45 12 Demand 10 15 12 14 5. Don Yale, president of Hardrock Concrete Company has plants in three locations and is currently working on three major construction projects located at different sites. The shipping cost per truckload of plant capacities and project requirements are provided in the accompanying table. Formulate an initial feasible solution to Hardrock's transportation problem using the northwest corner rule. Project Plant 1 A B C $10 $4 $11 Plant Capacity 70 4 2 $12 $5 $8 50 3 $9 $7 $6 30 40 50 60 150 Project Requirement 6. The top speed Bicycle Co. manufactures and market a line of 10 speed bicycles nationwide. The firm has final assembly plant in two cities, New Orleans and Omaha. If three major warehouses are located near the large market are of New York, Chicago, and Los Angeles. The sale requirements for the next year at the New York warehouse are 10,000 bicycle, at the Chicago warehouse 8,000 bicycle, and at the Los Angeles 15,000 bicycles. The factory capacity at each location is limited. New Orleans can assembles and ship 20,000 bicycles, the Omaha plant can produce 15,000 bicycles per year. The cost of shipping one bicycle from each factory to each warehouse differ and these unit shipping costs are as follows To New York Chicago New Orleans Los Angeles $2 $3 $5 $3 $1 $4 From Omaha The company wishes to develop a shipping schedule that will minimize its total annual transportation cost