length of pool --- x
width of pool -----y
cost = 10x + 5y = 1000
2x + y = 200
y = 200-2x
area = xy
= x(200-2x)
= 200x - 2x^2
d(area)/dx = 200 - 4x
= 0 for a max of area
4x=200
x=50
then y = 200-100 = 100
state your conclusion
This summer Borice decides to put a rectangular swimming pool in his back yard. The material he uses for the border of the length of the pool costs $10 per foot and the material he uses for the width costs $5 per foot. He would like spend $1,000 on the perimeter of the pool. Given these constraints, what are the dimensions of the pool (length and width) that will maximize the surface area of his pool?
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