Question

A manufacturer wants to enlarge an existing manufacturing facility such that the total floor area is 1.5 times that of the current facility. The floor area of the current facility is a rectangular and measures 300 feet (length) by 140 feet (width). The manufacturer want to increase each dimension by the same amount.

(a) Write a function that represents the new floor area A. (Use x as the variable)

(b) Find the dimensions of the new floor. (Round your answers to two decimal places.)

(c) Another alternative is to increase the current floor's length by an amount that is twice an increase in the floor's width. The total floor area is 1.5 times that of the current facility. Repeat parts (a) and (b) using this criteria.

Answer 1

a) If the current dimensions are 140 x 300 ft, and each dimension is to be increased by x ft, the new dimensions will become (140+x) x (300+x) ft. Therefore the new floor area will be A = (140+x)(300+x) or 42000 + 440x + x^2 ft.

b) Since we know that this new area is 1.5 times that of the old area:
42000 + 440x + x^2 = 1.5(140)(300)
42000 + 440x + x^2 = 63000
x^2 + 440x - 21000 = 0
x = 43.44 ft
Therefore, the new width is 140+x = 183.44 ft, and the new length is 300+x = 343.44 ft.

c1) If we increase the width by x, then we increase the length by twice this amount, or 2x. Our area will then be A = (140+x)(300+2x) = 42000 + 580x + 2x^2.
c2) If this is 1.5 times the original area:
42000 + 580x + 2x^2 = 1.5(140)(300)
42000 + 580x + 2x^2 = 63000
2x^2 + 580x - 21000 = 0
x = 32.55
So the width is 140+x = 172.55 ft, and the length is 300+2x = 365.10 ft.