Please solve A,B,C,D, & E. Show all work.
A.) Define x, y , and z
B.) Give the system of linear equations for this problem
C.) List the augmented matrix that corresponds with your system in part b
D.) Use \"rref\" on your calculator to find the row reduced form of your augmented matrix and give it below.
E.) What is the final answer to the problem in the context of the problem.
3. A private investment club has S200,000 earmarked for investment in stocks. To arrive at an accept- able overall level of risk, the stocks that management is considering have been classified into three categories: high risk, medium-risk, and low-risk. Management estimates that high-risk stocks will have a rate of return of 15% per year; medium-risk stocks, 10% per year; and low risk stocks, 6% per year. The members have decided that the investment in low-risk stocks should be equal to the sum of the investments in the stocks of the other two categories. Determine how much the club should invest in each type of stock if the investment goal is to have a return of $20,000 per year on the total investment. (Assume that all the money available for investment is invested.)
x is the money invested in high risk stocks; Returns are 15% pa
y is the money invested in medium risk stocks; Returns are 10% pa
z is the money invested in low risk stocks; Returns are 6% pa
Also one constraint is x+y=z; (low risk investment = medium + high risk investment)
Also x+y+z <= 200,000 (total investment fund available)
And 0.15x + 0.1 y + 0.06z = 20,000 (total returns)
Augmented matrix is (200,000 , 20,000) T
Putting z= x+y we get
0.15x + 0.1 y + 0.06x+ 0.06y = 20,000
0.21x + 0.16y = 20,000
210 (x/1000) + 160 (y/1000) = 20,000
We see that x= 80,000 and y= 20,000
210*80 + 160*20 = 16800+ 3200 = 20,000
Thus x=80,000 and y = 20,000;
Now z= x+y = 80,000+ 20,000 = 1,00,000
Final Answer:
Thus invest 80,000 in high risk investments; 20,000 in medium risk investments and 1,00,000 in low risk investments;
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