we know that the area , this is our constraint. call it equation (1)
we want to be as economical as possible, so let's make one of the shorter sides of the fence the $12 per foot part.
thus, the cost for this side is 12W, and the cost for the other 3 sides is 6(2L + W), thus, the total cost C is,
from equation (1), we have that , thus
.......this is the function we want to minimize
thus we find C' as set it equal to zero and solve for L. then we can find W using the fact that W = 270/L
Let the length of the package be and the side length of the end beA parcel delivery service will deliver a package only if the length plus the girth (distance around) does not exceed 100 inches. Find the maximum volume of a rectangular box with square ends that satisfies the delivery company's requirements.
then the girth is and the length is
thus we want , this is our constraint
Now, the volume is given by
from our constraint, we see that
thus, ........this is the function we want to maximize
thus we find and set it equal to zero and solve for , then we can find
Note that, for the maximum, we use the = sign as opposed to the sign