# Math Help - Quadratic Modelling Help

I need a little help with b) ii.
http://img10.imageshack.us/img10/1038/73...

a) i A=y(8+x)-x^2
ii P=2x+2y+16
b) i A=192+16x-2x^2

Thanks

2. Originally Posted by user_5
I need a little help with b) ii.
http://img10.imageshack.us/img10/1038/73...

a) i A=y(8+x)-x^2
ii P=2x+2y+16
b) i A=192+16x-2x^2

Thanks
Simply solve equation b) for x, and those are the allowable x values. Quadratic formula.

3. Solving for x using the quadratic formula gives.

$x=4 \pm 4\sqrt7$

0<x<12

4. Originally Posted by user_5
Solving for x using the quadratic formula gives.

$x=4 \pm 4\sqrt7$

Since P = 64 you have y = 24 - x. Also, from the diagram it's clear that you require $y \geq x$.
These two things can only happen if $0 \leq x \leq 12$.
And since $A > 0$ is satisfied for these values of x, $0 \leq x \leq 12$ is the answer.