What is the meaning of "girth" of a rectangular box?
Here's an optimization problem.
A parcel delivery service will deliver a package only if the length plus the girth (distance around, taken perpendicular to the length) does not exceed 112 inches. Find the maximum volume of a rectangular box with square ends that satisfies the delivery company's requirements.
I have a few issues with it, but mainly I don't know what the "girth" of the box is. I think I have a general idea of what to do after I learn what that is.
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$\begingroup$Let us say we have a box. We know that the volume is $l \cdot w \cdot h$.We know that we are trying to optimize this problem with the constraint that $2 w+2 h+l$ is $112$. We know that the base is a square so the volume is now $l^2 h$. We also happen to know that $w=h$. So we have $4w+l=112$. We can isolate the constraint as such: $l=112-4w$. We then get this cubic $(112-4w)^2 \cdot w$. I am sure that you can do the rest.
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