Question

Mr. Jones has to invest in three types of​ stocks, low-risk,​ medium-risk, and​ high-risk. He invests according to three principles. The amount invested in​ low-risk stocks will be at most more than the amount invested in​ medium-risk stocks. At least will be invested in​ low- and​ medium-risk stocks. No more than will be invested in​ medium- and​ high-risk stocks. The expected yields are ​% for​ low-risk stocks, ​% for​ medium-risk stocks, and ​% for​ high-risk stocks. How much money should Mr. Jones invest in each type of stock to maximize his total expected​ yield?

Answer 1

Since the numbers are missing, I looked for a similar question:

Mr. Jones has $9000 to invest in three types of stocks: low-risk, medium-risk and high-risk. He invests according to the following rules: the amount invested in low-risk stocks will be at most $1000 more than the amount invested in medium-risk stocks. At least $7000 will be invested in a combination of low- and medium-risk stocks. No more than $7000 will be invested in a combination of medium- and high-risk stocks. The expected annual returns are 6% for low-risk stocks, 7% for medium-risk stocks, and 8% for high-risk stocks. How much should he invest in each type of stock to maximize his total expected yield?

let:

L = low risk stocks

M = medium risk stocks

H = high risk stocks

maximize 0.06L + 0.07M + 0.08H

L + M + H ≤ 9000

L ≥ M + 1000

L + M ≥ 7000

M + H ≤ 7000

using solver, the optimal solution = 4,000L + 3,000M + 2,000H , which yields a maximum profit = $610

Mr. Jones should invest $4,000 in low risk stocks, $3,000 in medium risk stocks and $2,000 in high risk stocks.