A landscaper is asked to design and build a fenced in rectangle flower bed. The flower bed is to be make up of two different varieties of flower with one forming a 2 foot border around the other. The garden's owner already has a 100ft square of flower she wants to use on the outside border. Since these flowers are already paid for, the landscaper's only profit will come when he makes from selling the fence and inner flowers. The landscaper should choose the dimensions of the bed to maximize the cost to the owner. If fencing cost $25 for each foot length and the second flower variety cost $38 per ft^2. what is the maximum possible cost for such a garden???
Optimization problems?
100 sq feet minus 16 square feet for the corners =84
84 / 2 = 42 linear feet of border
42 / 4 = 10.5
so the inner section will be
10.5 by 10.5 or 110.25 sq feet
the border will be 14.5 by 14.5
The fence on the perimeter of that will be 58 feet long (14.5 x 4)
110.25 x 38 = $4189.50
58 x 25 = $1450
4189.50 +1450 = $5639.5
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