a.)find the value of x when the monthly profits is at a maximum.
b.)find the maximummonthly profit.
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f,4 quadratic functions
2009-10-25 7:34 am
the monthly profits $P of a factory is given by P= -4x^2+2000x-8000, where x is the number of items produced per month.
a.)find the value of x when the monthly profits is at a maximum.
b.)find the maximummonthly profit.
a.)find the value of x when the monthly profits is at a maximum.
b.)find the maximummonthly profit.
回答 (1)
2009-10-25 7:44 am
✔ 最佳答案
P= -4x^2+2000x-8000a) by the method of completed square
P= -4x^2+2000x-8000
=-4(x^2-500x+2000)
=-4[x^2-500x+(500/2)^2-(500/2)^2-2000]
=-4[(x-250)^2-62500-2000]
=-4[(x-250)^2-64500]
=-4(x-250)^2+258000
if x=250, the factory has the maximum monthly profit .
b) put x=250 into P=-4(x-250)^2+258000,
we have P=-4(250-250)^2+258000
=-4x0+258000
=258000
the maximun monthly profit is $258000
2009-10-28 09:51:45 補充：
a) by the method of completed square
P= -4x^2+2000x-8000
=-4(x^2-500x+2000)
=-4[x^2-500x+(500/2)^2-(500/2)^2+2000] <--對不起，正負號弄錯了。
=-4[(x-250)^2-62500+2000]
=-4[(x-250)^2-60500]
=-4(x-250)^2+242000
if x=250, the factory has the maximum monthly profit .
2009-10-28 09:51:53 補充：
b) put x=250 into P=-4(x-250)^2+242000,
we have P=-4(250-250)^2+242000
=-4x0+242000
=242000
the maximun monthly profit is $242000
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