A financier plans to invest up to $7 million in three projects. She estimates that project A will yield a return of 5% on her investment, project B will yield a return of 10% 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 total investment. 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?
A) Project A: $1,350,000, project B: $1,350,000, and project C: $2,900,000; maximum profit: $690000
B) Project A: $2,850,000, project B: $2,900,000, and project C: $1,350,000; maximum profit: $230,000
C) Project A: $1,400,000, project B: $2,800,000, and project C:$2,800,000; maximum profit: $910,000
D) Project A: $2,800,000, project B: $2,800,000, and project C: $1,400,000; maximum profit: $700,000

Question

A financier plans to invest up to $7 million in three projects. She estimates that project A will yield a return of 5% on her investment, project B will yield a return of 10% 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 total investment. 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? ​
A) Project A: $1,350,000, project B: $1,350,000, and project C: $2,900,000; maximum profit: $690000
B) Project A: $2,850,000, project B: $2,900,000, and project C: $1,350,000; maximum profit: $230,000
C) Project A: $1,400,000, project B: $2,800,000, and project C:$2,800,000; maximum profit: $910,000
D) Project A: $2,800,000, project B: $2,800,000, and project C: $1,400,000; maximum profit: $700,000

Quizplus · Accepted Answer

Given the constraints and the goal to maximize returns, investing $2,800,000 in projects A and B, and $1,400,000 in project C adheres to all the financier's conditions while maximizing returns. Project A must be at least 60% of the total investment, but investing more in the lower yield Project A than necessary would not maximize returns. Project C, offering the highest return, should receive the maximum allowed investment (20% of $7 million = $1.4 million). The remaining funds are then split between Projects A and B to maximize returns while adhering to the constraint that the sum of investments in B and C should not exceed 60% of the total investment. The maximum profit calculation aligns with these investment amounts.

A Financier Plans to Invest Up to $7 Million in Three