Question

Fair weather airlines has a peculiar rule about luggage. it will accept only bags for which the sum of the length l and width w is at most 36 inches, while the sum of length l, height h, and twice the width w is at most 72 inches. what are the dimensions of the bag with the largest volume that fair weather will accept?

a) l = in
b) w = in
c) h = in

Answer 1

To find the dimensions of the bag with the largest volume that Fair Weather Airlines will accept, we can set up an optimization problem. The bag dimensions that maximize volume are l = 18 inches, w = 18 inches, and h = 18 inches. Therefore, the correct answer is not provided in the options.

Step-by-step explanation:

To find the dimensions of the bag with the largest volume that Fair Weather Airlines will accept, we can set up an optimization problem. Let l, w, and h represent the length, width, and height of the bag, respectively.

Fair Weather Airlines has two constraints:

1. l + w ≤ 36 inches

2. l + h + 2w ≤ 72 inches

We want to maximize the volume V = lwh. To simplify, we can express h in terms of l and w using the first constraint: h ≤ 36 - l.

Substitute this into the second constraint: l + (36 - l) + 2w ≤ 72, simplifying to 2w ≤ 36 or w ≤ 18.

So, the bag dimensions that maximize volume are l = 18 inches, w = 18 inches, and h = 18 inches. Therefore, the correct answer is not provided in the options.