Problem #1. At American Airlines the size limit of a bag is calculated by adding

Question

Problem #1. At American Airlines the size limit of a bag is calculated by adding the total outside dimensions of a bag: length + width +height. The checked baggage allowance is 62 inches. We want to check in a bag with a square base In your solution follow these steps and answer the questions: Solution (1) Express the volume of the bag as function of the length of one side of the base. Denote this length by x. (2) Draw the volume function here. Use appropriate scaling and appropriate labeling on the axes. (3) Use your graphing calculator to determine the dimensions of a bag that will give the maximum volume What are the three dimensions of the bag at maximum volume? (4) What is the maximum volume? Display it on the graph.

Explanation / Answer

(1)

Square base side = a

height = h

Let the maximum allowance is to be utilized so

a + a + h = 62

h = 62 - 2a

volume = heigh x width x length = a2 (62-2a)

(2)

(3)

for maximum volume, first derivative w.r.t. a is 0, so

V = 62a2 - 2a3

dV/da = 124a - 6a2=0

a = 20.67 inch

h = 20.67 inch

all of them same would give the maximum volume

(d)

max volume = 8,826.96 inches3

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