A financier plans to invest up to $600,000 in two projects. Project A yields a return of 9% on the investment x dollars, whereas project B yields a return of 16% on the investment of y dollars. Because investment B is riskier than investment A, the financier has decided that the investment in Project B should not exceed 40% of the total investment. How much should she invest in each project to maximize the return on her investment P in dollars, and what amount is available for investment?

Project A = $240,000

Project B = $360,000

Explanation:

Planned Investment amount = $600,000

Project A = x dollars, with 9% return

Project B = Y dollars, with 16% return

Project B should not exceed 40% of total investment amount

Therefore, if y dollars is spent on project B,

(600,000 - y) is spent on project A

Return on project A :

0.09(600,000 - y) = 54,000 - 0.09y

Return on project B :

0.16y

Total return = return on A + return on B

54,000 - 0.09y + 0.16y

Total return = 54,000 + 0.07y

Note: Project B should not exceed 40% of investment, Therefore,

y <= 0.4(600,000)

y <= 240,000

slope of the function is positive '54,000 + 0.07y', total return increases when y increases.

Therefore return on investment will be maximized when y = 240,000, as it should not exceed 40% for project B and the rest 360,000 can be invested in project A.