1959 WordsJan 9, 20138 Pages

EM 505 - Decision Models, Fall 2012 Homework 3 - December 10-11, 2012
1. The diagram below depicts a system of aqueducts that originate at three rivers (nodes R1, R2 and R3) and terminate at a major city (node T) where the other nodes are junction points in the system. Using units of thousands of acre feet, the tables below show the maximum amount of water that can be pumped through each aqueduct per day and the following diagram shows the network of the system. From/To A R1 75 R2 40 R3 B 65 50 80 C 60 70 From/To D A 60 B 70 C E 45 55 70 F 45 90 From/To T D 120 E 190 F 130
The city water manager wants to determine a flow plan that will maximize the flow of water of the city. Formulate this problem as a max flow problem by identifying a*…show more content…*

Formulate the problem as a mixed integer programming model to minimize the total processing time on the machine while satisfying all the pertinent constraints.
1 2 3
4 5 6
Figure 1
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Product 1
Product 2
10. The board of directors of the General Wheels Co. is considering seven large capital investments. These investments differ in the estimated long-run profit (net present value) they will generate, as well as in the amount of capital required, as shown by the following table (in units of millions of dollars). Investment Opportunity 1 2 3 4 5 Estimated profit Capital required 17 43 10 28 15 34 19 48 7 17
6 13 32
7 9 23
The total amount of capital available for these investments is $100.000.000. Investment opportunities 1 and 2 are mutually exclusive, and so are 3 and 4. Furthermore, neither 3 nor 4 can be undertaken unless either 1 or 2 is undertaken. There are no such restrictions on investment opportunities 5, 6 and 7. The objective is to select the combination of capital investments that will maximize the total estimated long-run profit (net present value). Formulate the BIP model for this problem. 11. A company sells seven types of boxes, ranging in volume from 17 to 33 cubic feet. The demand and size for each box type are as the following: Box 1 Size 33 Demand 400 2 30 300 3 26 500 4 24 700 5 19 200 6 18 400 7 17 200
The variable cost (in dollars) of producing each box type is equal to the volume of the box. A fixed

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