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Maths help!

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astarmathsandphysics:
When i get home

SGVaibhav:
omg

i had some very similiar kinda question.

it was about finding the maximum profit using derivatives.

astarmathsandphysics:
The costs of a firm which makes climbing boots are of two kind:
-Fixed cost (plant rates, office expenses): $2000 per week;
-Production costs (material, labour): $20 for each pair of boots made.
Market research suggest that if they price the boots at $30 a pair they will sell 500 pairs a week, but that at $55 a apair they will sell none at all; and between these values the graph of sales against profit is a straight line.
If they price boots at $x pair (30<x<55) (inclusive) find expressions for
a) weekly sales,
b) the weekly reciepts
c) the weekly costs
assuming that just enought boots are made
hence showing that the weeklly profit, $P, is given by
P=-20x2+ 1500x-2400.
Find the price at which the boots should be sold to maximise the profit.
a)sales=-20x+1100
b)receipts=sales*prce=x(-20x+1100)
c)costs=20x+2000
   
Surely something I have not understood. Are you sure " the graph of sales against profit is a straight line" is correct from the question?

f

tmisterr:
yes thats what the question says!!

SGVaibhav:
Stuck on 1 question for like 1.5 hours
i mean 1 hour 30 mins

lim  t-->2   (   (t^3 + 3t^2 - 12t + 4)  / (t^3 - 4t)    )


[in english]
(t(cube)   +  3t(square) - 12t + 4)       divided by   (t(cube) - 3t)
when the lim of t approaches 2

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