An aquaculture company is designing a rectangular treatment tank with an open top. The tank is to have a base where the length is exactly twice the width. Let the width of the base be www metres and the height of the tank be hhh metres.
Given that the capacity of the tank is fixed at 288 m3288 \text{ m}^3288 m3:
Show that the total internal surface area, S m2S \text{ m}^2S m2, of the tank is given by
S=2w2+864w S = 2w^2 + \frac{864}{w} S=2w2+w864Use algebraic differentiation to find the value of www for which SSS has a stationary point.
Justify by further differentiation that this value of www gives a minimum internal surface area for the tank.
