CaliforniaStatePolytechnicUniversity, POMONA

Industrial and Manufacturing Engineering Department

EGR 549 MIDTERM EXAM Date: 5-2-07

Last name: First name:

Instructions: Read all the questions carefully. Organize your work clearly, neatly, and legibly. Show all details of your work. Identify your answers. Do not write on the back of any page. This is a closedbook and closed note exam. You may have two sheets of information. The total score is 50 points.

Good Luck

Dr. Parisay

1- (5 points) Use NWC heuristic to find initial basic feasible solution for the following balanced transportation tableau.

demand 1 / demand 2 / demand 3 / demand 4 / Demand 5
supply 1 / 13 / 8 / 7 / 10 / 0
5000
supply 2 / 9 / 5 / 12 / 3 / 0
6000
supply 3 / 14 / 6 / 4 / 15 / 0
2500
supply 4 / 2 / 17 / 1 / 11 / 0
2000
5500 / 4500 / 1500 / 1500 / 2500

2- ( 5 points) Prepare the following constraints for the first simplex tableau.

Max Z = 35 X1 + 15 X2

S.T.

12 X1 - X2 >= 22

5X1 + 7X2 = 200

3X1 + X2 =< 15

3-( 10 points) Star Oil is considering five different investment opportunities. The cash outflows and net present values (in millions of dollars) are given below. Star Oil has $50 million available for investment now (time 0), it estimates that one year from now (time 1) $25 million will be available for investment. Star Oil may purchase any fraction of each investment. In this case, the cash outflows and NPV are adjusted accordingly. For example if Star Oil purchases one-fifth of investment 3, then one-fifth of cash outflow at time 0, one-fifth of cash flow at time 1, and one-fifth of NPV should be considered. Star Oil wants to maximize the NPV that can be obtained by investing in investments 1 – 5.

Investment ($)

1 2 3 4 5

Time 0 cash outflow1153 5 529

Time 1 cash outflow 3 6 5 134

NPV1316181439

This problem is formulated and solved, using WinQSB. Input and output are as below.

Xi = fraction of investment i purchased by Star Oil

Input:

Output:

a) How the optimal solution and O.F. will change if the NPV of investment 3 is decreased to $15?

b) Draw a sensitivity graph for possible changes in available total investment for this year (year 0).

c) Write a report to a manager and explain your findings. Assume the manager is not familiar with OR field.

(on separate sheet)

4- (10 points) A company faces the following demands during the next three periods. Period 1 for 20 units, period 2 for 25 units, and period 3 for 50 units. The unit production cost during each period is $15. A holding cost of $2 per units is assessed against each period’s ending inventory. At the beginning of period 1, the company has 8 units on hand. The company requires 9 units left as inventory for future at the end of period 3. The company’s customers can consider back order (backlog) of their demand with a penalty cost of $3 for each unit per period. Company can consider subcontracting during each period which will cost $20 per unit. The maximum capacity of production in each period is 22 units and maximum subcontracting is 10 units per period. Create a transportation tableau to represent this problem.

(on separate sheet)

5- (10 points) Rylon Corporation manufactures Brute and Chanelle perfumes. The raw material needed to manufacture each type of perfume can be purchased for $5 per pound. Processing 1 lb of raw material requires 2 hour of 1aboratory time. Each pound of processed raw material yields 4 oz of Regular Brute Perfume and 6 oz of Regular Chanelle Perfume. Regular Brute can be sold for $8/oz and Regular Chanelle for $11/oz. Rylon also has the option of further processing Regular Brute and Regular Chanelle to produce Luxury Brute, sold at $35/oz, and Luxury Chaneelle, sold at $44/oz. Each ounce of Regular Brute processed further requires an additional 0.5 hours of laboratory time and $11 processing cost and yields 1 oz of Luxury Brute. Each ounce of Regular Chanelle processed further requires an additional 0.7 hours of laboratory time and $14 processing cost and yield 1 oz of Luxury Chanelle. Each year, Rylon should fulfill the union contract by using a minimum 95000 hours of laboratory worker and can purchase up to 40000 lb of raw material. Each hour of laboratory worker will cost $35. Formulate an LP problem to maximize profit.

6- (10 points) Sunco manufactures five types of gasoline: LFR, LFP, LR, LP and LL. The time required to produce a batch of gasoline depends on the type of gasoline last produced and is given in the table below (in minutes).

Use WinQSB to determine the order in which the gasolines should be produced each day so that it minimizes the total time of production (change over). Print input and output. Write a report for a manager and explain your findings. Assume the manager is not familiar with OR field. (your time limit 15 minutes)

Last-Produce Gas to Be Next Produced .

GasolineLFRLFPLRLPLL

LFR - 50120 14040

LFP 60 -140110125

LR 90130 - 6095

LP 130120 80 -75

LL 50 110 95 85-