Question

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 400 feet of fencing available for the three sides that require fencing. How long will the longest side of the restaurant be?b. What is the maximum area?

Answer 1

Supposing the side parallel to the museum is L, and the other two sides that we want to fence are 2W, this would L+2W.

L+2W=400

L=400-2W

Area= LW

So,

Area=(400-2W)W

Area=400W-2W^2

Since this is a quadratic equation, the graph opens downwards because -2W^2. The maximum occurs at the vertex of the parabola.

Vertex of a paraboa is given by:

x=-2/2a

remember a quadratic equation is:

ax^2+bx+c

So

W=-400/2(-2)=100

W=100, So the longest side would be L=400-2(100)=200

Area of a rectangle is LW, so the maximum area would be

A=200*100=2000 ft^2