Jeff is willing to invest $6,000 in buying shares and bonds of acompany to gain maximum returns. From his past experience, heestimates the relationship between returns and investments made inthis company to be:
R = –2S2 – 9B2– 4SB + 20S + 30B.      Â
where,
R = total returns in thousands of dollars
S = thousands of dollars spent on Shares
B = thousands of dollars spent on Bonds
Jeff would like to develop a strategy that will lead to maximumreturn subject to the restriction provided on the amount availablefor investment.
a. What is the value of return if $4,000 is invested in sharesand $2,000 is invested bonds of the company?
b. Formulate an optimization problem that can be solved to maximizethe returns subject to investing no more than $6,000 on both sharesand bonds.
c. Determine the optimal amount to invest in shares and bonds ofthe company. How much return will Jeff gain? Round all your answersto two decimal places.
