A trust fund is planning to invest up to 6000 in two types...

A trust fund is planning to invest up to $6000 in two types of bonds.: A and B. Bond A is safer than bond B and carries a dividend of 8% while bond B carries a dividend of 10%. Suppose that the bond’s rule state that no more than $4000 may be invested in bond B, while at least $1500 must be invested in bond A. The amount invested in bond B cannot exceed one half the amount invested in bond A. How much should be invested in each type of bond to maximize the fund’s return?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Transcript

00:02 All right, this question gives some information about different investments and their return.

00:08 So our profit equation says that investment a returns 8%, and investment b returns 10 % annually.

00:23 So that's our objective function.

00:25 But it also says that our total budget is 250.

00:30 Okay, so a plus b has to be less than or equal to 250 ,000.

00:43 But then it also says that at least one -fourth of the portfolio has to be a stock, and at least a fourth has to be b stock.

00:58 So that says that a and b both have to be bigger than a quarter of the total amount we have to invest.

01:10 Which in this case is 62 ,500.

01:18 So now that we have this, i graphed our region over here, subject to our constraints, which i have right here, and our feasible region is right here.

01:36 So we see that our vertices are these three sides of the triangle.

01:46 So our first vertex right here is the bare minimum we could invest, the second vertex is 187 -50 -60 -6200.

02:21 So that's investing our full budget into our a stock, but putting the bare minimum into b stock.

02:29 And then our final vertex does the opposite pretty much.

02:37 We put the bare minimum into a and put everything else into b.

02:44 So now we just need to calculate the profitability of each...

Question

Please give Ace some feedback