Fair Weather Airlines will accept only bags for which the sum of the length and width is 51 inches, while the sum of length, height, and twice the width is 102 inches. What is the largest volume of the bag that it will accept Round your answer to the nearest whole number.
A)14,739 cubic inches
B) 19,652 cubic inches
C) 24,565 cubic inches
D) 9,826 cubic inches
E) 4,913 cubic inches

Question

Fair Weather Airlines will accept only bags for which the sum of the length and width is 51 inches, while the sum of length, height, and twice the width is 102 inches. What is the largest volume of the bag that it will accept  Round your answer to the nearest whole number.  
A)14,739 cubic inches
B) 19,652 cubic inches
C) 24,565 cubic inches
D) 9,826 cubic inches
E) 4,913 cubic inches

Quizplus · Accepted Answer

To find the largest volume, we need to maximize the product of length, width, and height given the constraints. Solving the system of equations: L + W = 51 and L + H + 2W = 102, we find L = 51 - W and H = 51 + W. The volume V = L * W * H = (51 - W) * W * (51 + W). Maximizing this expression gives the largest volume, which is approximately 19,652 cubic inches.

Fair Weather Airlines Will Accept Only Bags for Which the Sum