A science museum is going to put an outdoor restaurant along one wall of the museum. The restaurant space will be rectangular. Assume the museum would prefer to maximize the area for the restaurant.
a) suppose there is 120 feet of fencing availible for the three sides that require fencing. How long will the longest side of the restaurant be?
b) what is the maximum area?
2007-03-05 11:53:51 · 1 answers · asked by Anonymous in Education & Reference ➔ Homework Help
A = l * w
fencing = 2w + l = 120 ft
Let's redefine the fencing equation to find l in terms of w.
2w + l = 120 ft
l = 120 - 2w
Plug into our area:
A = lw = (120 - 2w) * w
A = 120w - 2w^2
A = 0 when w = 0 and 60, so the maximum area lies at the midpoint = where w = 30.
fencing = 2w + l = 60 + l = 120. l = 60 (longest side)
A = 120(30) - 2(30)^2 = 3600 - 1800 = 1800 sq ft (area)
2007-03-06 03:07:10 · answer #1 · answered by ³√carthagebrujah 6 · 0⤊ 0⤋