Re: [微分] 應用問題x2
※ 引述《s1990716 (小婷)》之銘言：
: 1.Marginal Profit
: When the price of a glass of lemonade at a lemonade stand was $1.75,
: 400 glasses were sold. When the price was lowered to $1.50, 500 glasses
: were sold. Assume that the demand function is linear and that the variable
: and fixed cost are $0.10 and $25,respectively.
variable and fixed cost?
先了解定義才能做
: Find the profit P as a function of x,the number of glasses of lemonade sold.
這一題不確定題意是不是這樣
我的理解是這樣
total cost c = 0.1x + 25
demand function is $ = $(x)
1.75 = 400a + b
1.50 = 500a + b
=> a = -0.0025
b = 2.75
P = x*$ - c
= x*(-0.0025x + 2.75) - (0.1x + 25)
: 2.Depreciation
: The value V of a machine t years after it is purchased is inversely
: proportional to the square root of t+1. The initial value of the machine is
: $10,000.
: a.Write V as a function of t
V = a / (t+1)^2
t = 0 , V = 10000
=> V = 10000 / (t+1)^2
: b.Find the rate of depreciation when t=1
Rate(t) = dV/dt = -20000 / (t+1)^3
Rate(t=1) = -20000 / 8 = -2500 ($/yr) (minus sign means depreciation)
: 煩請各位高手解惑~~~
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