Jeff Is Willing to Invest $5000 in Buying Shares and Bonds

Essay

Jeff is willing to invest $5000 in buying shares and bonds of a company to gain maximum returns. From his past experience, he estimates the relationship between returns and investments made in this company to be:
R = -2S² - 9B² - 4SB + 20S + 30B.
where,
R = total returns in thousands of dollars
S = thousands of dollars spent on Shares
B = thousands of dollars spent on Bond
Jeff would like to develop a strategy that will lead to maximum return subject to the restriction provided on amount available for investment.
a. What is the value of return if $3,000 is invested in shares and $2,000 is invested bonds of the company?
b. Formulate an optimization problem that can be solved to maximize the returns subject to investing no more than $5,000 on both share and bonds.
c. Determine the optimal amount to invest in shares and bonds of the company. How much return will Jeff gain? Round all your answers to two decimal places.