We did a problem similar to this in class without the conditions of the heat admission.
A house in the shape of a rectangular box is to hold 10,000 cubic feet. The four walls admit heat aat 5 units per minute per square foot. The roof admits heat at 3 units per minute per square foot. The floor admits heat at 2 units per minute per sq ft. What should the dimensions (length, width, height) of the house be in order to minimize the rate(units per minute) at which heat enters the house?
This might help but I'm not sure if we need it or not. The equation to find surface area of a rectangle
S=2xy+2xz+2yz
This is Calculus 3 actually so I'm afraid it's not that simple.
I know how to minimize the function of S finding the dimensions for x, y and z. But I don't know how to interpret the heat into the problem correctly. Can you help me with that? I know that the four sides of the rectangle must be smaller than the roof and floor.
A house in the shape of a rectangular box is to hold 10,000 cubic feet. The four walls admit heat aat 5 units per minute per square foot. The roof admits heat at 3 units per minute per square foot. The floor admits heat at 2 units per minute per sq ft. What should the dimensions (length, width, height) of the house be in order to minimize the rate(units per minute) at which heat enters the house?
This might help but I'm not sure if we need it or not. The equation to find surface area of a rectangle
S=2xy+2xz+2yz
This is Calculus 3 actually so I'm afraid it's not that simple.
I know how to minimize the function of S finding the dimensions for x, y and z. But I don't know how to interpret the heat into the problem correctly. Can you help me with that? I know that the four sides of the rectangle must be smaller than the roof and floor.
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Ms,
I can skype this problem a LOT easier than type it if
you let me know how to contact you.
I tutor free online since moving to France from Florida in June 2011.
Hope this is most helpful and you will continue to allow me to tutor you.
If you dont fully understand or have a question PLEASE let me know
how to contact you so you can then contact me directly with any math questions.
If you need me for future tutoring I am not allowed to give out my
info but what you tell me on ***how to contact you*** is up to you
Been a pleasure to serve you Please call again
Robert Jones.............f
"Teacher/Tutor of Fine Students"
I can skype this problem a LOT easier than type it if
you let me know how to contact you.
I tutor free online since moving to France from Florida in June 2011.
Hope this is most helpful and you will continue to allow me to tutor you.
If you dont fully understand or have a question PLEASE let me know
how to contact you so you can then contact me directly with any math questions.
If you need me for future tutoring I am not allowed to give out my
info but what you tell me on ***how to contact you*** is up to you
Been a pleasure to serve you Please call again
Robert Jones.............f
"Teacher/Tutor of Fine Students"