A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and co
rporate bond fund, and the third is a T-bill money market fund that yields a rate of 8%. The probability distribution of the risky funds is as follows: Expected Return Standard Deviation Stock fund (S) 20 % 30 % Bond fund (B) 12 15 The correlation between the fund returns is 0.10. a-1. What are the investment proportions in the minimum-variance portfolio of the two risky funds.
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Answer:
The Linear programming model is given as below
Profit Function:
Constraints:
Explanation:
As the question is not complete, the complete question is found online and is attached herewith.
Let the number of product 1 to be produced is X, that of product 2 is Y and product 3 is Z
so the maximizing function is the profit function which is given as
Now as the number of hours in a week are 40 and there are a total of 10 type 1 machines so the total number of machine 1 hours are 40*10=400 hours
As from the given table product 1 uses 2 machine hours of machine 1, product 2 uses 2 machine hours of machine 1 and product 3 uses 1 hour of machine 1 so
Now as the number of hours in a week are 40 and there are a total of 6 type 2 machines so the total number of machine 2 hours are 40*6=240 hours
As from the given table product 1 uses 3 machine hours of machine 2, product 2 uses 4 machine hours of machine 2 and product 3 uses 6 hour of machine 2 so
Now as the number of hours in a week are 40 and there are a total of 8 type 3 machines so the total number of machine 3 hours are 40*8=320 hours
As from the given table product 1 uses 4 machine hours of machine 3, product 2 uses 6 machine hours of machine 3 and product 3 uses 5 hour of machine 3 so
Now as the machine 1 is used as 2X+2Y+Z in a week and the week is of 40 hours so the number of machines to be used are given as
Now as the machine 2 is used as 3X+4Y+6Z in a week and the week is of 40 hours so the number of machines to be used are given as
Now as the machine 3 is used as 4X+6Y+5Z in a week and the week is of 40 hours so the number of machines to be used are given as
Now the workers are available for 35 hours so the worker available at the machine 1 is given as
That of machine 2 is given as
That of machine 3 is given as
As the total number of workers is 19 so the constraint is given as
So the Linear programming model is given as below
Profit Function:
Constraints:
