The postal service will accept a box for domestic shipment only if the sum of its length and girth (distance around) does not exceed 99 in. Suppose that you have a box with square sides so that its dimensions are h by h by w and the girth is 2h+2w, such a box is shown to the right. Complete part (a) and (b). a. What dimensions will give the box its largest volume? b. Graph the volume as a function of h and compare what you see with your answer in part (a). Girth (distance around here) a. Let h denote the length of the box and w denote the width, set up the equation of the volume of the box, V. v = ☐ When h= inches and winches, the box has largest volume. (Type integers or decimals.) b. Choose the correct graph of the volume V as a function of h below. ○ A. B. Q 8000- 6000- 4000- 2000- 0- 0 11 22 33 ✓ 8000- 6000- 4000- 2000- 0- 0 11 22 33 ✓ 8000- 6000-1 4000- 2000- 0- 0 11 22 33 ✓ W h ○ D. Q 8000- 6000- 4000- 2000- 0- 0 11 22 33
The postal service will accept a box for domestic shipment only if the sum of its length and girth (distance around) does not exceed 99 in. Suppose that you have a box with square sides so that its dimensions are h by h by w and the girth is 2h+2w, such a box is shown to the right. Complete part (a) and (b). a. What dimensions will give the box its largest volume? b. Graph the volume as a function of h and compare what you see with your answer in part (a). Girth (distance around here) a. Let h denote the length of the box and w denote the width, set up the equation of the volume of the box, V. v = ☐ When h= inches and winches, the box has largest volume. (Type integers or decimals.) b. Choose the correct graph of the volume V as a function of h below. ○ A. B. Q 8000- 6000- 4000- 2000- 0- 0 11 22 33 ✓ 8000- 6000- 4000- 2000- 0- 0 11 22 33 ✓ 8000- 6000-1 4000- 2000- 0- 0 11 22 33 ✓ W h ○ D. Q 8000- 6000- 4000- 2000- 0- 0 11 22 33
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section12.5: Analytic Steady-state Queueing Models
Problem 17P
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Transcribed Image Text:The postal service will accept a box for domestic shipment only if the sum of its length and
girth (distance around) does not exceed 99 in. Suppose that you have a box with square sides so
that its dimensions are h by h by w and the girth is 2h+2w, such a box is shown to the right.
Complete part (a) and (b).
a. What dimensions will give the box its largest volume?
b. Graph the volume as a function of h and compare what you see with your answer in part (a).
Girth (distance around here)
a. Let h denote the length of the box and w denote the width, set up the equation of the volume of the box, V.
v = ☐
When h=
inches and winches, the box has largest volume.
(Type integers or decimals.)
b. Choose the correct graph of the volume V as a function of h below.
○ A.
B.
Q
8000-
6000-
4000-
2000-
0-
0
11
22 33
✓
8000-
6000-
4000-
2000-
0-
0
11 22 33
✓
8000-
6000-1
4000-
2000-
0-
0
11
22
33
✓
W
h
○ D.
Q
8000-
6000-
4000-
2000-
0-
0 11
22
33
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