Linear Programming Investment Problem - YouTube

Now we're going to work on an investment problem you have twelve thousand dollars

to invest and three different funds from which to choose the municipal bond fund

has a 7% return the local bank CD's have an 8% return and the high risk account

has an expected I hope for return of 12% to minimize risks we decide not to

invest any more than two thousand dollars in the high-risk account for tax

reasons you need to invest at least three times as much in the municipal

bonds as in the bank CD's assuming the year-end yields are as expected what is

the optimal investment amounts so again the first thing we're going to do is

identify the variables we're going to say B is the amount we invest in the

bonds C is the amount we invest in the CDs and H is the amount invested in the

high-risk account our objective function what we want to do is we want to

maximize our revenue and letter to maximize our revenue we're going to take

seven percent times the amount invested in bonds eight percent times the amount

invested in the CDs and twelve percent times the amount invested in the

high-risk subject to the total available is the bond the amount invested in bonds

CDs and the high risks has to be less than or equal to twelve thousand dollars

it says that we have to invest less than we want to invest you wouldn't decide to

invest less than twenty two thousand dollars in high risk the tax

requirements to invest at least three times as much your municipals as CD so

bonds has to be greater than or equal to three times the amount invested in CDs

since we want our variables all on the left-hand side of the inequality we

subtract receipt from both sides so B minus three C has to be greater than or

equal to zero again all the variables the B the C and the H have to be

positive numbers so we make them greater than or equal to zero setting this up we

initialize the values of zeros for all of our variables

the amount invested in the bonds the CDs and the high-risk has to be no less than

zero we put in the 7% the 8% in the 12% which are the returns for these

investment we put the amount for the bonds the CDs the high-risk has to be

great less than or equal to twelve thousand dollars high risk that's one

has to be less than or equal to two thousand the mountain bonds that's one

minus three times c0 for the high risk has to be greater than or equal to zero

bonds has to be greater than or equal to zero C DS is greater than or equal to

zero and high risks has to be greater than or equal to zero now we're going to

set up our equations in order to evaluate the algebraic expressions so

again we have that the 7% times the amount invested in bonds and we want

that to be a fixed sell so we can copy it to the constraints plus the the

return on the CDs which is the 8% times the amount invested in CDs and again we

go to make that a big sell and lastly the 12% times the amount invested in the

C in the high risk again which is zero and again we want that to be a fixed

sell we notice that that is zero and then we're going to copy this down and

we want to make sure that it's correct so we click on the cell and we notice we

have one times zero one times zero one times zero which is what we want we'll

try one more and we have one times zero negative 3 times zero and zero times

zero so it looks like it's correct now we're going to go to data and we're

going to open up solver in order to be able to determine how we're going to

solve this particular system of inequality equations where it says set

objective we click on cell K 13 14 because that is where we evaluated the

objective function it goes automatically to

maximize and we want to maximize the values associated with the amount we put

in the bonds the CDs and the high-risk funds and make sure you're in the

correct window so let's do that again the objective function is in cell K 14

we're maximizing go to the window for the B C and H that's the zeros and we

have subject to our constraints now looking at the constraints we have the

information over here that we are going to add the constraints so we're going to

add the constraint for the total amount invested where we have 0 has to be less

than or equal to the $12,000 we add the high risk constraint which says 0 has to

be less than or equal to the $2,000 we add the tax requirement constraint which

says 0 has to be greater than or equal to the 0 that we had there we add the

constraints for the the trivial constraints so we have that the B has to

be greater than or equal to 0 we add the C again has to be greater than or equal

to 0 let's put the box over there and lastly we want to make sure that we have

the H all right and I want to make sure that it's in the right place so I have

the 20 and this should also be 20 and lastly we want the H to be greater than

or equal to let's get that correct greater than or equal to again 0 and we

finish we press ok now I want to watch to make sure that I did everything

correctly so I have the K on the left hand side of the inequality I have the J

on the right hand side and we have row 16 and 17 or less than or equal to

everything else should be greater than or equal to

I noticed that 20 I have the wrong side so I click on here I change it and I'm

just going to change the sign to greater than or equal to I press ok now all the

constraints look correct I go to simplex I ask it to solve the

equation and we are noticing that we should invest $7,500 in municipal bonds

$2,500 in CDs and $2,000 in the high-risk account for the maximum return

or Rev or profit of nine hundred and sixty-five dollars