416 IE Last name:
California State Polytechnic University, POMONA Industrial and Manufacturing Engineering Department FINAL EXAM Date: 3-17-03 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 closed-book and closed-note exam. You may have one sheet of information. The total score is 35 points. Good Luck Dr. Parisay 1- General Ford has three plants, three warehouses, and three customers. The location of these are as follows: Plants: Det, Atl, and Den; Warehouses: San, New, and Los; Customers: Nash, Chic, and Phil Cars are produced at plants, then shipped to warehouses, and finally shipped to customers. The following tables provide information on capacity of production at each plant, amount of demand for each customer, cost of shipment of one car from each location to the other, and optimal solution using WinQSB. (8 points) Demand Solution requirements
From 1 Det 2 Atl 3 Atl 4 Den 5 San To Flow Unit Cost Total Cost New 150 6 900 San 60 8 480 Unused_Supply 40 0 0 San 200 7 1400 Nash 100 20 2000 160 80 70 16 21 13 2560 1680 910 9930 Nash Chic Phil San 20 17 16 New 21 13 18 Los 19 22 23 Demand 180 70 160
6 San Phil 7 New Nash 8 New Chic Total Objective
Supply capacity
Det Atl Den San New Los Supply 13 6 15 150 8 10 9 100 7 11 12 200
Function Value =
a) Represent this optimal solution graphically.
b) Write a report to a manager who is not familiar with this field (do not use terms specific to this field) and explain the solution. Try to extract as much information as possible!!
2- A problem is formulated as follows: (7 points)
O.F. max Z = 20x1 + 2x2 s. t. 2x1 + 5x2 <= 11 X1, X2 >= 0; X1, X2 integer Perform Branch-and-Bound method to cover up to three nodes. IF YOU CANNOT SOLVE THE FIRST PROBLEM: Assume that the first subproblem is solved and the optimal solution is found to be: Z = 200, X1 = 3.4, and X2 = 10.9. How will you branch for the next iteration of branch-and-bound method? Draw the tree and clearly indicate you're the new subproblems be to solved later.
3- Powerco has three electric power plants that supply the needs of four cities. The transportation tableau for the optimal solution (to minimize the total cost) is as below. The cost of sending 1 mkwh of electricity from a plant to a city is indicated in the top right corner of each cell of the following tableau. The optimal shipment plan is indicated in the bottom left corner of each cell. Answer to the questions about the effect of each change in original information. You should indicate the effect on the basis, basic feasible solution, and optimal value of the objective function. (10 points)
City 1 Plant 1 Plant 2 45 Plant 3 45 28 10 20 18 30 16 10 18 24 5 32 30 30 10 40 City 2 12 25 26 14 50 City 3 20 City 4 18 35
a) The demand of City 3 and the supply of Plant 2 is increased by 10 mkwh. What is the effect of this change?
b) How much can we change the demand of City 3 and the supply of Plant 3 so that we have the same basis. What is the effect of this change on optimal solution?
c) The cost of shipment from Plant 2 to City 2 is increased to 30. What is the effect of this change on the optimal solution.
d) How much the cost of shipment from Plant 1 to City 2 can change so that the basic feasible solution (shipment plan) does not change?
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