math problem?
A sicience museum is going to put an outdoor resturant along one wall of the meuseum. the restaurant space will be rectangular. Assume the museum would prefer to maximize the area for the resturant.
a) Suppose there is 120 feet of fencing avaible for the three sides that requrie fenching how long will thw longest side be?
b) What it the maximum area?
please show work
Comments
x+2y = 120
x*y = Area
A = (120-2y)*y
dA/dy = 120 - 4y
for maxima, dA/dy = 0 ==> prove maxima, d^2A/dy^2 = -4 (proved)
therefore, 120 - 4y = 0
y = 30 ft
therefore, x = 120 -2*30 = 60 ft
Max Area = 30*60 = 1800ft^2
30 30 60 60
total area = 1800 sq ft
The fence will make up the following sides: 30 30 60
I solved it by "zeroing in" via Excel