Question

Test soon! Calc optiminaztion problem. Please help!

A French aquarium is to be built with a rectangular slate bottom twice as
long as it is wide, and with four rectangular glass sides. There is no top. Slate for the
bottom costs $2 per square meter while the glass used cost $4 per square meter. Find the
dimensions of the cheapest tank having a volume of 18 cubic meters.

Answer 1

let x be width of the base then 2x is the length let h be depth
so V = 2x*x*h = 2x^2h

18 = 2x^2 h
h = 18/2x^2 = 9 / x^2

Answer 2

now find an expression for the cost of the material
are of the base = 2x^2 so cost will be 2*2x^2 = 4x^2
area of the 4 sides = 2hx + 4hx = 6hx
so cost = 4 * 6hx = 24hx

Answer 3

now you can plug in h = 9 / x^2 into the formula for the cost
differentiate with respect to x , equate to zero and find value of x for minimum cost

Answer 4

Oh they've gone!