12.1-4. The board of directors of General Wheels Co. is consid- ering six large
ID: 2572562 • Letter: 1
Question
12.1-4. The board of directors of General Wheels Co. is consid- ering six large capital investments. Each investment can be made only once. These investments differ in the estimated long-run profit (net present value) that 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 2 3 4 5 6 Estimated profit 15 12 16 18 9 11 Capital required 38 33 39 45 23 27 The total amount of capital available for these investments is $100 million. Investment opportunities 1 and 2 are mutually exclusive. and so are 3 and 4. Furthermore, neither 3 nor 4 can be undertaken e unless one of the first two opportunities is undertaken. There are no such restrictions on investment opportunities 5 and 6. The ob- ective is to select the combination of capital investments that will maximize the total estimated long-run profit (net present value) (a) Formulate a BIP model for this problem. C (b) Use the computer to solve this model.Explanation / Answer
option : 1
Investment 1 and 2 are mutually exclusive and neither 3 nor 4 can be undertaken unless one of the first two opportunities i.e. 1 or 2 is under taken. So, 1 and 2 , 1 is more profitable than 2. So, we take 1. In 3 or 4, 4 is more profitable than 3.So, we take 4. Here we select 1 and 4.
Total Investent required in 1 and 4 = 38 + 45 = 83
Total earnings = 15+18 = 33
Amount left for investment = 100-83 = 17
Now with the amount left for investment, we cannot take any other project.
Option : 2
If we take investment 1 and 3, then amount left for investment = 100 -38-39 = 23
Now with the amount left for investment, we can take project 5.
Total investment = 38+39+23 = 100
Total earnings = 15+16+9 = 40
Option : 3
If we take investment 2 and 3, then amount left for investment = 100 -33-39 = 28
Now with the amount left for investment, we can take project 6.
Total investment = 33+39+27 = 99
Total earnings = 12+16+11 = 39
Option : 4
If we take investment 2 and 4, then amount left for investment = 100 -33-45 = 22
Now with the amount left for investment, we cannot take any project.
Total investment = 33+45 = 78
Total earnings = 12+18 = 30
So, answer is option 2 where total investment required is 100 and earnings is 40. We should select 1,3 and 5.
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