SET UP BUT DO NOT SOLVE THE FOLLOWING LINEAR PROGRAMMING PROBLEM.

Question

A financier plans to invest up to $500,000 in two products. Project A yields a return of 10% on an investment, whereas Project B yields a return of 15% on the investment. 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 in order to maximize her return? What is the maximum return?

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I'm pretty sure that the profit function is P=0.1A+0.15B

And part of the "subject to" is A+B≤500,000
A≥0, B≥0

But I can't figure out how to apply the part in which "Project B should not exceed 40% of the total investment."

Answer 1

40% of total investment
= 40%*500000
= 200000
This puts a ceiling on B, and a lower bound on A.