Hello, newbie here. I need help bad y'all. I was given an optimization problem and it is due Tomorrow. I thought I had it figured out so I was about to turn it in until another classmate said the answer was different due to adding the area of the spheres on the end using 2/3piR^3. They did not know how to solve it, but knew the answer was around 21.07 or 20.07. I need a detailed explanation of how to get the answer. I have been working on it for hours and cannot figure it out and I have 5 finals this week. Thank you in advance!!
The question is "you are asked to design a fuel tank for a fighter jet that will hold 300 liters of jet fuel. The shape of the tank is a tube with rounded ends (this is where the spheres are) a cylinder with two hemispheres attached to each end. The side (the cylinder part) cost $.1 cm^2 to make while the rounded tops (hemisphere) cost $.3 per cm^2 to make. You will find out the radius of the tube that will minimize the manufacturing cost.
Find optimal radius and show your work
explain each step
explain how solution would change with the change in the total amount of fuel
The question is "you are asked to design a fuel tank for a fighter jet that will hold 300 liters of jet fuel. The shape of the tank is a tube with rounded ends (this is where the spheres are) a cylinder with two hemispheres attached to each end. The side (the cylinder part) cost $.1 cm^2 to make while the rounded tops (hemisphere) cost $.3 per cm^2 to make. You will find out the radius of the tube that will minimize the manufacturing cost.
Find optimal radius and show your work
explain each step
explain how solution would change with the change in the total amount of fuel