CPM Homework Help : CALC Problem 5-39

YELLOW SUBMARINE, Part One

Ring O. Star was sick and tired of chasing blue meanies around the inside of his yellow submarine, so he decided to build a special detention chamber to hold the ones he caught. The first design he thought of was a rectangular chamber with sides made of razor-sharp barbed wire. To save money, he decided to build the chamber up against a submarine wall - that way only three sides needed to be made out of barbed wire. He estimated the detention chamber should have $40$ square meters of area. What dimensions should the chamber have so that Mr. Star can buy the least amount of barbed wire?

Hint:

You are being asked to 'minimize' perimeter. Did you recognize that this is an optimization problem?
The first thing you will do is build a geometric equation that represents the situation. Then you will apply Calculus.

Geometry Step:

What do we know?

Calculus step:

Now that we have an equation, $P\left(h\right)$ , let's find it's minimum value.
$P^\prime(h)$ = ___________________
To find the $h$ -value of the max and min, set $P^\prime(h) = 0$ , and solve for $h$ .
Then, for a complete answer, don't forget to find the corresponding value of $b$ .