A woman wants to design a rectangular vegetable garden with an ornamental fence around it.?
The fencing for
three sides of the garden costs $ 2/foot. The fencing for the fourth side costs $ 3/foot. She has $ 210 to spend
on the fence. What dimensions should she give the garden to maximize its area?
Best answer:
Answer by Dylan D
Let one side be x and the other be y. (x, y > 0)
2(2x+y) + 3y = 210
4x + 5y = 210
5y = 210 - 4x
y = 42 - 0.8x
x = 52.5 - 1.25y
xy = (42 - 0.8x)(52.5 - 1.25y) = 2205 - 42x - 52.5y + xy
2205 - 42x - 52.5y = 0
42x + 52.5y = 2205
42x + 70y = 210* 14 = 2940
17.5y = 375
y =~ 21.43
x =~ 25.71
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