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A company wishes to manufacture a box with a volume of 36 ft^3 that is open on top and is twice as long as it is wide. Find the dimensions of the box produced from the minimum amount of material.
I must have missed class the day we went over this. I have no clue how this is supposed to be done. Please help!
Sorry, I'm not really understanding this. My question asks me to "write an equation for the quantity you are supposed to minimize," and also to "find a function for what I'm supposed to minimize" too. So would...h = 18/x^2 be the equation and then the function would be what you wrote with the surface area?
The base area is . The area of each side on the side with width x is xz and the area of each side on the side with width y is yz= 2xz so the total surface area is .
Finally, you are told that the volume is to be 36 cubic feet: the volume is given by so . Putting that into the equation for A, we have . That is the "equation for the quantity you are supposed to minimize" and the function is .