求解微積分(原文題目商類)

[匿名]

2010-01-13 10:41 am

when the admission price to a theater was 180 dollars per ticket, 1000 tickets were sold. when the price was raised to 200 dollars, only 800 tickets were sold.
Assume that the demand function is linear and the variable costs are 10 dollars and the fixed costs are 120,000 dollars. Find the profit P as a function of x which denotes the numbers sold, and the marginal profit when x = 500.

我自己所翻的意思是
當票價180元時，可賣出1000張票
當200元時可賣出800張票
假定需求函數屬線性，且變動成本10元，固定成本120,000元
則當邊際利潤x=500時，利潤P表示賣出票數的函數x為何?

我不太確定翻的對不對
不過我算了好久怎麼算都算不出那個170的答案啊orz

拜託幫幫忙告訴我到底怎麼算的

回答 (2)

問題管理員

2010-01-14 10:43 am

無最佳解答

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myisland8132

2010-01-13 9:57 pm

Demand function y=A+Bx
Sub. x=180, y=1000 ; x=200, y=800
We have A+180B=1000 ; A+200B=800 =>A=2800,B=-10

Profit = Revenue-Cost
=x(A+Bx)- (120000+10x)
=(2800-10x)x-(120000+10x)
=-10x^2+2700x-120000

dP/dx=-20x+2700. when x=500,marginal profit = 1700

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