Question

Find max and min

Answer 1

Can someone help me find P3_min and P3_max
\[\left[\begin{matrix}100 & 100&100 \\ 200 & 100&0\\ 100&0&200\end{matrix}\right]*\left(\begin{matrix}d1 \\ d2\\d3\end{matrix}\right)=\left(\begin{matrix}100 \\ 100\\P3\end{matrix}\right)\]

Where d1,d2,d3≥0

Answer 2

And d1+d2+d3=1

Answer 3

Anyone?

Answer 4

@perl Can you help me?

Answer 5

this is a max and min problem?

Answer 6

Yes I need to find min and max P3

Answer 7

why is it called min and max

Answer 8

we can solve the augmented matrix

Answer 9

I know the result is 0<P3<150. But I cant find at way to show it

Answer 10

If we /100 we get
\[\left[\begin{matrix}1 & 1&1 \\ 2 & 1&0\\ 1&0&2\end{matrix}\right]*\left(\begin{matrix}d1 \\ d2\\d3\end{matrix}\right)=\left(\begin{matrix}1 \\ 1\\P3/100\end{matrix}\right)\]

Answer 11

whats the name of this class

Answer 12

Math finance..

Answer 13

maybe if you could write more details of the chapter and stuff i could google it.

Answer 14

perlll!!!!! lol

Answer 15

we have the three equations
d1 + d2 + d3 = 1
2d1 + d2 = 1
d1 + 2d3 = p3/100

d2 = 1 - 2*d1,
d3 = 1/2* (p3/100 - d1)
so plugging that into our first equation we have
d1 + (1-2*d1) + 1/2 (p3/100 - d1) = 1

Answer 16

looks like an elementary linear algebra problem

Answer 17

@UsukiDoll I agree :) But I cant sole it.

Answer 18

umm reduce row echelon form it?

Answer 19

ah... ok first multiply the d column with that 3x3 matrix and then reduce row echelon it.

Answer 20

it's not in REF form...hmm need an upper triangular matrix

Answer 21

you see the triangles? that's the main diagonal...anything below the main diagonal must be 0 for it to be in REF form.