04 Jun Question A simple way to model the construction of an oil tanker is to start with a large rectangular sheet of steel that is x feet wide and 3x feet long. Now cut a s
Question
A simple way to model the construction of an oil tanker is to start with a large rectangular sheet of steel that is x feet wide and 3x feet long. Now cut a smaller square that is t feet on a side out of each corner of the larger sheet and fold up and weld the sides of the steel sheet to make a traylike structure with no top.
a. Show that the volume of oil that can be held by this tray is given by
V = t (x -2t )(3x -2t) =3tx2-8t 2x 9+4t3.
b. How should tbe chosen so as to maximize V for any given value of x?
c. Is there a value of x that maximizes the volume of oil that can be carried?
d. Suppose that a shipbuilder is constrained to use only 1,000,000 square feet of steel sheet to construct an oil tanker. This constraint can be represented by the equation 3×2 – 4t 2= 1,000,000 (because the builder can return the cut-out squares for cr
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