A pension fund manager decides to invest a total of at most

A pension fund manager decides to invest a total of at most $25 million in U.S. Treasury bonds paying 4% annual interest and in mutual funds paying 7% annual interest. He plans to invest at least $5 million in bonds and at least $ 10 million in mutal funds. Bonds have an initail fee of $100 per million dollars, while the fee for mutual funds is $200 per million. The fund manager is allowed to spend no more than $4000 on fees. How much should be invested in each to maximize annual interest? What is the maximum annual interest?

The amount the should be invested in Treasury bonds is $___million and the amount that should be invested in mutual funds is $___ million.

The maximum annual interest is $___.

Solution

Let x be the amount invested in US treas bonds and y in mutual funds

x>5 and y >10

Intial fee for x = 100x and for y is 200y

100x+200Y<4000

OR x+2y<40

Objective is to maximise z = 0.04x+0.07y

Subject to all constraints, x>5, y>10 and x+2y<40

we solve algebraiclly that

(5. 17.5) or (20,10) are the corner points

For (5,17.5) interest = 0.20+1.225 = 1.425

For (20,10) interest = 0.8+0.7 =1.5

Hence The amount should be invested in teasury bonds = 20 million

Mutual funds = 10 million

Max interest = 1.5 million