Answer:
The "maximum annual interest" is "1536.15 million dollars".
Explanation:
Let "t" represent the "money" (in millions) invested in "US Treasury bonds" and "f" the "money" (in millions) invested in "mutual funds".
t ≥ 0
f ≥ 0
A "pension fund manager" decided to "invest a total" of at most "$ 3535 million" in "US Treasury bonds" paying "66% annual interest" and in "mutual funds" paying "99% annual interest".
t + f ≤ 40
t ≥ 5
f≥ 15
Bonds which have an "initial fee of $100 per million dollars", while "the fee for mutual funds" is "$200 per million". The "fund manager" is permitted to spend no more than "$66000 on fees".
100t + 200f ≤ 66000 divide both sides by 100
t + 2f ≤ 660
The annual interest is described with the objective function:
F (t, f) = 0.66t + 0.99f
We have the following constrains:
t ≥55
f ≥ 1515
t + f ≤3535
t + f ≤ 660
The corner points are: (55, 1515)
Evaluating the function at the corner points, we find:
F(55, 1515) = 0.66 × 55 + 0.99 × 1515 = 136.3 + 1499.85 = 1536.15
The "objective function", represents "revenue", is maximized when "t = 55" and "f = 1515 ".
The manager should invest 55 million in US Treasury bond and 1515 millions in mutual funds.
The "maximum annual interest" is "1536.15 million dollars".