Precalc question

Question

You have $6000 with which to build a rectangular enclosure with fencing. The fencing material costs $20 per meter. You also want to have two parititions across the width of the enclosure, so that there will be three separated spaces in the enclosure. The material for the partitions costs $15 per meter. What is the maximum area you can achieve for the enclosure?

Answer 1

2w at 15$/m

+2W+2L at 20$/m

=6g

2w15+2(W+L)20=6000

WL=?

Answer 2

Let x = length and y = width

20(2x) + 20(2y) + 15(2y) = 6000

40x + 70y = 6000

70y = 600 - 40x

So, y = (60 - 4x) / 7

Area = A = xy = (60x - 4x²) / 7 = -(4/7)x² + (60/7)x

The graph of A is a parabola opening downward. The maximum occurs when x = -(60/7) / (-8/7) = 7.5

Maximum area when x = 7.5 m and y = 30/7 m