The dimensions of the rectangular enclosure are 60 feet and 75 feet and the maximum area of each half of the enclosure is 2250 feet².
From the information given, the cost of the higher fence is represented as:
= 8(2w + 2l) = 16w + 16l
The cost of the lower fence will be 4w.
The relationship between the length and width will be illustrated thus:
2400 = 16w + 16l + 4l
2400 = 20l + 16w
Divide through by 4
600 = 4l + 5w
Express l in terms of the width.
l = 150 - 1.25w
The area will be:
= (150 - 1.25w) × w
= 150w - 1.25w²
The maximum area will be where the vertex of the parabola is. They are w1 = 0 and w2 = 120.
The width of the fence is 60 feet. The length will be:
= 1/4(600 - 5 × 60)
= 75 feet
The area of the lower fence will be:
= 1/2 × 60 × 75
= 2250 feet²
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