Re: Trignomy word problem

Hello, Niaboc!

I'll set it up . . .

Quote:

A pension fund manager decides to invest a total of at most $39 million

in Treasury Bonds paying 4% annual interest and in Mutual Funds paying 8% annual interest.

He plans to invest at least $5 million in Trasury Bonds and at least $10 million in Mutual Funds.

Treasury Bonds have an initial 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 $5000 on fees.

How much should be invested in each to maximize annual interest?

What is the maximum annual interest?

Let $\displaystyle x$ = amount invested in Treasury Bonds (in millions of dollars): $\displaystyle x\ge\,0$

Let $\displaystyle y$ = amount invested in Mutual Funds (in millions of dollars): .$\displaystyle y \,\ge\,0$

Total invested, $39 million: .$\displaystyle x + y \:\le\:39$

Invest at least $10 million in Mutual Funds: .$\displaystyle x \,\ge\,10$

Invest at least $5 million in Treasure Bonds: .$\displaystyle y \,\ge\,5$

Fee for Treasury Bonds: $\displaystyle 100x$

Fee for Mutual Funds: $\displaystyle 200y$

Maximum fee, $5000: .$\displaystyle 100x + 200y \,\le\,5000 $

Maximize interest: .$\displaystyle I \:=\:0.04x + 0.08y$