✔ 最佳答案
The cost of producing x watches is $（120-50x+2x2）.If each watch is sold at a price of $（150-x）.
a.Write a function f(x) (in dollars) to represent the total profit in selling x watches.
Cost of producing x watches
= $(120 - 50x + 2x2) 【Given】
Income of selling x watches
= $(150-x)(x)
= $(150x - x2)
Profit of selling x watches
= income - cost
= $(150x - x2) - $(120 - 50x + 2x2)
= $(150x - x2 - 120 + 50x - 2x2)
= $(-3x2 + 200x - 120)
So f(x) = -3x2 + 200x - 120.
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b.what is the profit if 15 watches are produced and sold？
From (a), f(x) = -3x2 + 200x - 120
Put x = 15 into f(x),
The profit of 15 watches are produced and sold
= f(15)
= -3(15)2 + 200(15) - 120
= -675 + 3000 - 120
= 2205
So the profit is $2205.
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c.How many watches should be sold in order to attain a maximum profit？What is the maximum profit？
From (a),
f(x) = -3x2 + 200x - 120
f'(x) = d(-3x2 + 200x - 120)/dx
f'(x) = -3(2x) + 200(1) + 0
f'(x) = -6x + 200
As the coefficient of x2 < 0 of f(x), so the turning point of f(x) is a minimum point.
The minimum f(x) is at f'(x) = 0.
When f'(x) = 0
-6x + 200 = 0
x = 200/6
x = 100/3 (33.33333)
As 100/3 is not an integer, but the number of watches (x) should be an integer.
So we consider the nearest integer, which is 33.
So 33 watches should be sold to attain the maximum profit.
Maximum profit
= f(33)
= -3(33)2 + 200(33) - 120
= -3267 + 6600 - 120
= 3213
So the maximum profit is $3213.
2007-01-09 21:30:41 補充：
講解：ＰＡＲＴ Ａ＝＝＝＝＝＝part a 意思是說賣 x 隻錶的成本是 $(120-50x+2x²)，而每隻錶售價是 $(150-x)。要求的是 profit function f(x)。計算 profit 首先要得出 cost 和 income。製作 x 隻錶的 cost 已知 = $(120-50x+2x²)。賣去 x 雙錶的 income 是 $(150-x) 乘以 x。根據 profit = income - cost，可得出 f(x)。
2007-01-09 21:31:08 補充：
ＰＡＲＴ Ｂ＝＝＝＝＝＝part b 要求得出製作和賣出 15 隻錶的 profit。從 a 得出 profit function f(x)，只要將 x = 15 代入 f(x) 就能得出所需 profit。
2007-01-09 21:32:44 補充：
字數所限，其餘的我會寄信給你 ^^
