Chapter 4.1, Problem 50E

ASSET ALLOCATION A financier plans to invest up to $\$2\text{million}$ in three projects. She estimates that Project A will yield a return of $10\%$ on her investment, Project B will yield a return of $15\%$ on her investment, and Project C will yield a return of $20\%$ on her investment. Because of the risks associated with the investments, she decided to put not more than $20\%$ of her total investment in Project C. She also decided that her investments in Projects B and C should not exceed $60\%$ of her total investment. Finally, she decided that her investment in Project A should be at least $60\%$ of her investments in Projects B and C. How much should the financier invest in each project if she wishes to maximize the total returns on her investments? What is the maximum amount she can expect to make from her investments?