Close sidebar webwork/mat145f19stern/hw13/5 hw13: problem 5 previous problem problem list next problem (1 point) 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 104 inches. find the maximum volume of a rectangular box with square ends that satisfies the delivery company's requirements.

The volume in such a package is 10,415.41 in³

Step-by-step explanation:

Consider the provided information.

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 104 inches.

Let the dimension are x by x by y.

Where x is the variable for the square base package and y is the variable for length.

Thus l=x, b=x and h=y

Then the volume of the box is: (∵V=lbh)

The maximum combined length and girth is 104.

Therefore,

Substitute the value of y in volume of the box.

Substitute V'(x)=0.

Now apply second derivative test.

(Min)

(Max)

If x=52/3 then

Substitute x = 52/3 and y = 104/3 in

Hence, the volume in such a package is 10,415.41 in³