Question

Formulate but do not solve the following exercise as a linear programming problem. A financier plans to invest up to $500,000 in two projects. Project A yields a return of 11% on the investment of x dollars, whereas Project B yields a return of 14% on the investment of y dollars. Because the investment in Project B is riskier than the investment in Project 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?

Answer 1

Project B yields more than Project A. If they were equally risky he would chose B.
However we are told that because project B is riskier, it should not exceed 40% of $500,000.

Investment in project A is 0.60 *$500,000 = $300,000 which we call x
Investment in project B is 0.40 *$500,000 = $200,000 which we call y

Project A yields 11% on x dollars which is 0.11 * $300,000 = $33,000
Project B yields 14% on y dollars which is 0.14 * $200,000 = $28,000
Max return on the investment subject to this restraint is $61,000