Hi, Im having a problem finishing off a problem. It is a calc ab problem

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 4 meters and its volume is 36 cubic meters. If building the tank costs $10 per square meter for the base and 5$ for the sides, what is the cost of the least expensive tank?

So the information i gathered was:

SA=LW+2(LH+WH)

W=4

V=36

S0 since V=LWH=36, 4LH=36, L=9/H

Then, SA= 36/h+18+8h

At first i thought I would just need to optimize that and go -36h^-2 + 8 and found the min was at 2.121 but then I thought you might need to factor in the price using another equation. Could someone help me with this problem?