Lisa has a total of $200,000 to invest in three types of mutual funds: growth, b

Question

Lisa has a total of $200,000 to invest in three types of mutual funds: growth, balanced and global funds. Growth funds have a rate of return of 12% per year, balanced funds a rate of return of 10% per year, and global funds a return rate of 8% per year. To help diversify her portfolio and control risk, Lisa has decided the following: all of the $210,000 will be invested, at most one third of her total portfolio is to be in global funds, at most half in balanced funds, and at least $40,000 must be invested in growth funds. She also wants the amount invested in growth funds to be less than the amount invested in balanced funds. a) Formulate a Linear Program to solve the problem above. Include the following: a precise definition of decision variables and a verbal description of the constraints. b) Give the data table. c) Use a guess and check approach to find a feasible solution, you do not have to find an optimal solution. note: please show how you arrived to the answer, please & thank u

Explanation / Answer

decision: to increase the returns in each investment subject to the constraints. If x is the amount invested in Growth funds, y is the amount invested in balanced funds, z is the amount invested in Global funds. The returns for each investment is as follows: Maximize (12*x + 10*y + 8*z)/100 subject to the constraints, z < 70000$ (at most one third of her total portfolio is to be in global funds) y < 105000$ ( at most half in balanced funds) x > 40000$ ( at least $40,000 must be invested in growth funds) x - y < 0 (the amount invested in growth funds to be less than the amount invested in balanced funds) By guess and check method the solution is y = 104999$; x = 104998$, z = 3$. the profit can be calculated from the above decision equation. as to how I arrived at this solution, we have maximum returns for investment X, but X must be less than y, since thr is no lower limit on z I plan to keep it 0. to maximize x i shud maximize y whose upper limit is 105000$. hence y is 104999 (just less than 105000) and x

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