高数（英语题目）我们的高数作业如下～A manufacturer found that the sales figure

高数（英语题目）
我们的高数作业如下～A manufacturer found that the sales figure for a certain item depended on the selling price.The
market research department found that the maximum number of items that could be sold was
20,000 and that the number actually sold decreased by 100 for every $1 increase in price.The
total cost of production of the items consisted of a set-up cost of $20,000 plus $50 per item
manufactured.What price should be adopted to maximize profits,and how many items are
produced?
会做的帮个忙,作对了追加50分
答案是$125,7500..

设原价为p,涨价为x,利润为y
y=(p+x-50)(20000-100x)-20000
=20000p+20000x-1000000-100px-100x^2+5000x-20000
=20000p+25000x-100px-100x^2-1020000
令dy/dx=25000-100p-200x=0
x(max)=125-p/2
p最小值为0,x最大值为$125
20000-100x=20000-100*125=7500(items)

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