Linear Programming

Question

A woman seeks to invest no more than $20,000 of her savings in municipal bonds and mutual funds. The amount she will invest in municipal bonds will be at least three times the amount she will invest in mutual funds. However, she will invest no more than $5,000 in mutual funds. Under her constraints, which graph below indicates the possible ways the woman can invest her savings?

The constraints are:

(1) b > 0; f > 0 (i.e., no negative dollar values)

(2) b + f ≤ 20000 (i.e., total investment will be no more than $20,000)

(3) b ≥ 3f (i.e., the amount invested in municipal bonds will be at least three times that in mutual funds)

(4) f ≤ 5000 (i.e., no more than $5,000 invested in mutual funds)

Can someone show me how to graph these constraints?

Answer 1

If you let bonds be represented by the y-axis and mutual funds f by the x-axis, you would get a different graph. But use the same process.

Answer 2

Hi Brian,

Good job identifying the constraints!

The way you graph these, is to set up coordinate axes like you normally would for x and y, and instead of those, you label one axis 'b' and the other axis 'f'.

Then, you plot the lines:

b = 0

f = 0

b + f = 20.000 (you'll need to reformat this to look either like b = _____ or f = _____)

f = 5,000

For each line, then you shade in the inequality = ie. for b = 0, it'd be everything on the side of the f-axis that has positive values for b.

Where those shaded areas overlap, is your solution space for the problem.

Feel free to post back if you have followup questions!

-maurice