1. ## Optimization

A tank with a rectangular base and rectangular sides is to be open at the top. It is to be constructed so that its width is 4m and its volume is 36 cubic meters. If building the tank costs $10 per square meter for the base and$5 per square meter for the sides, what is the cost of the least expensive tank?

2. Originally Posted by meg24209
A tank with a rectangular base and rectangular sides is to be open at the top. It is to be constructed so that its width is 4m and its volume is 36 cubic meters. If building the tank costs $10 per square meter for the base and$5 per square meter for the sides, what is the cost of the least expensive tank?
I'll start you off.

Let the length be $x$
Let the height be $y$

Then the volume is: $V = 4xy = 36$ ---------> this is our constraint equation. solve for one of the variables and plug it into your objective equation (below).

We want to minimize cost, thus the cost equation is our objective.

Now $C = \underbrace{5(xy + xy + 4y + 4y)}_{\mbox{cost of the 4 sides}} + \underbrace{10(4x)}_{\mbox{cost of the base}}$

now simplify and minimize this function