Letdenote the amount invested at 6.75%. That means that (30,000 -xx) will be invested at 5%.

The allocation of funds between the two investments which would produce an aggregate return of exactly 6.5% would be described by the equation

0.065 = 0.0675x+ 0.05(30,000 -x). Solving for x gives the amount invested at 6.75% (with the remainder invested at 5%) that would yield exactly 6.5%.

Technically, the question would be modeled as an inequality, since the company needs the portfolio to yieldat least6.5%...

0.065<=0.0675x+ 0.05(30,000 -x) which would give you an answer of the form thatmust bex>=to some amount. But in this case, after solving the equality, it's common sense that this would represent the minimum that must be invested at 6.75%, because any shifting of funds from the 6.75% over to the 5% woulddecreasethe overall yield below the required target.