A simple way to model the construction of an oil tanker is to start with a large rectangle sheet of steel that is x feet wide and 3x feet long. Now cut a smaller square that is y 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.
I've shown that the volume can be represented by the equation:
V= 3tx^2 - 8t^2x +4t^3
b. How should t be 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?
I've solved parts a and d to this problem and now only b and c remain.
For b, I took the partial derivative of V with respect to x and solved for t, resulting in t=(3/4)x. this is clearly wrong, as the geometry doesn't quite work out. c seems to be dependent on the answer to b. This is in a Microeconomic text book in a section which summarizes the math needed for subsequent chapters. I'm just not sure how to approach this.
Any help would be GREATLY appreciated.
I've shown that the volume can be represented by the equation:
V= 3tx^2 - 8t^2x +4t^3
b. How should t be 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?
I've solved parts a and d to this problem and now only b and c remain.
For b, I took the partial derivative of V with respect to x and solved for t, resulting in t=(3/4)x. this is clearly wrong, as the geometry doesn't quite work out. c seems to be dependent on the answer to b. This is in a Microeconomic text book in a section which summarizes the math needed for subsequent chapters. I'm just not sure how to approach this.
Any help would be GREATLY appreciated.