CE AMATHS -DIFFERENTATION
2007-09-07 5:33 am
THE DISTANCE BETWEEN O AND A IS x km.The travelling cost of sending goods form A to O is proportional to x. And the rental cost for the factory is invesely proportional to x.When x = 2, the travelling cost is ＄1600 and the rental cost is ＄2500.
a) Let ＄C be the total rental and travelling cost of a factory at A. Show that C=800x+5000/x
b)Where A should be located so that the total rental and travelling cost of a factory is kept to minimum? How much is the minimum total cost?
回答 (1)
2007-09-07 5:49 am
✔ 最佳答案
Let C1 be the travelling cost and C2 be the rental cost.Hence, C1 = k1x and C2 = k2/x, where k1 and k2 are non-zero constant.
When x = 2, 1600 = k1(2), i.e. k1 = 800
2500 = k2/2, i.e. k2 = 5000
Therefore, total cost C = C1 + C2 = 800x + 5000/x
dC/dx = 800-5000/x^2 = 0
x^2 = 5000/800 = 6.25
x = 2.5 or -2.5(rejected)
d2C/dx2 = 10000/x^3
d2C/dx2 at (x = 2.5) > 0
Hence total cost is minimum when x = 2.5,
i.e. A should be located 2.5 km away from O.
參考: me
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