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

Why did you put b=1 and c=-3 in the tax requirements??

so we'll gonna ignore he farted at 3:13