PLEASE HELP QUICK WILL UPVOTE A parcel delivery service will deliver a package o

Question

PLEASE HELP QUICK WILL UPVOTE

A parcel delivery service will deliver a package only if the length plus girth (distance around) does not exceed 120 inches. (A) Find the dimensions of a rectangular box with square ends that satisfies the delivery service's restriction and has maximum volume. What is the maximum volume? (B) Find the dimensions (radius and height) of a cylindrical container that meets the delivery service's restriction and has maximum volume. What is the maximum volume? (A) The dimensions of the rectangular box arein (Use a comma to separate answers as needed.) The maximum volume is Dn3 (B) The radius of the cylinder is ? in. (Type an exact answer, using ? as needed.) The height of the cylinder isin. (Type an integer or a simplified fraction.) The maximum volume isin3 (Round to the nearest cubic inch as needed.)

Explanation / Answer

(A). Let the square have side s
Let the length be h

Let us assume that we use the maximum possible dimensions. That is,

4s + h = 120
v = hs2 = (120-4s)s2 = 120s2 - 4s3
dv/ds = 240s - 12s2 = 12s(20-s)
dv/ds = 0 when s = 20, h=40

V = (20)(20)(40)=16000

(B). Let r=radius and h=height

Then girth G=2?r
Volume V=?r2h

We know that G+h=2?r+h?120 as per regulation.
We will take G+h=120 to get the maximum and 'lose' the h
h=120?2?r

We can now express the volume in r only:
V=?r2h=?r2?(120?2?r)=120?r2?2?2r3

differentiating with respect to r

V'=240?r?6?2r2=6?r?(40??r)=0
40??r=0?r=40/? ? 12.73

Substituting:
G=2?r=80
h=120?80=40
V=?*(12.73)2*40=20364.16 which is approx to 20364

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.