last one!!!! abt calculous

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2007-01-24 6:17 pm

A small company manufactures crystal figurines. It can manufacture x thousand per week. If the selling price for each figurines is(21-2x) dollars and the total cost of manufacturing the figurines is (2000+176x+192x^2)dollars, find the number of figurines and the price that yields maximun profit.

回答 (1)

myisland8132

2007-01-24 6:25 pm

✔ 最佳答案

from the question, we have
the total earning for selling figurines
=1000x(21-2x)
the total cost of manufacturing the figurines is (2000+176x+192x^2) dollars
So the profit P
=1000x(21-2x)-(2000+176x+192x^2)
=21000x-2000x^2-2000-176x-192x^2
=-2192x^2+20824x-2000
dP/dx
=-4384x+20824
d^2P/dx^2=-4384<0
let dP/dx=0
-4384x+20824=0
x=4.75
Since d^2P/dx^2<0, we get the maximum value
So
the number of figurines that yields maximun profit is 4.75*1000=4750
and the selling price for each figurines is (21-2*4.75)=11.5 dollars

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