# Thread: other Functions problems help?

1. ## other Functions problems help?

Statement:
determine in 1000 is as P(x,y)=-2x^2-xy-y^2+8x+9y+10
where x is the amount spent on Radio and y is the amount spend on TV respectively. How much money should

Friends I CANT SOLVE it just give me method

Please friends this time help me!

thanks a lot

2. you need to take the partial derivatives of $P$ with respect to both $x$ and $y$

then in order to find the max equate them to zero, you will then have two equations together with two unknown terms, solve.

you should get two solutions in this case, just test which one will give you the max.

3. Originally Posted by Mauritzvdworm

you should get two solutions in this case, just test which one will give you the max.

4. $\frac{\partial P}{\partial x}=-4x-y+8$ and
$\frac{\partial P}{\partial y}=-x-2y+9$

now equate them to zero
$-4x-y+8=0$ so $y=-4x+8$ and
$-x-2y+9=0$ so

$-x-2(-4x+8)+9=0$ so $x=1$ and $y=4$

so you end up with the coordinate $(1,4)$ and if you test it it should give you the maximum.

5. Originally Posted by Mauritzvdworm
$\frac{\partial P}{\partial x}=-4x-y+8$ and
$\frac{\partial P}{\partial y}=-x-2y+9$

now equate them to zero
$-4x-y+8=0$ so $y=-4x+8$ and
$-x-2y+9=0$ so

$-x-2(-4x+8)+9=0$ so $x=1$ and $y=4$

so you end up with the coordinate $(1,4)$ and if you test it it should give you the maximum.

thanks man

6. Well, your original post mislead us. You said, highlighted in red, "just give me the method:" That is what Mauritzvdworm did in his first post. Apparently what you really wanted was the he do the problem for you.