Optimization Problem - Profit, please help!

Question

anonymous · Answer

attachment

freckles · Answer

well it looks like the demand function was suppose to be linear

freckles · Answer

not quadratic if that helps any

anonymous · Answer

1000(450-10x) ?

anonymous · Answer

1000(450-x) + 100(450-10x) ?

anonymous · Answer

I think I've got it - (450-10x)(1000+10x)

anonymous · Answer

nevermind that's wrong

anonymous · Answer

@Mertsj @ganeshie8 any idea on part A ?

dumbcow · Answer

you need to look at how price changes relative to change in quantity

you are given that if price decreases by 10 then sales goes up by 100
that is a slope of (-10/100) or (-1/10)

apply initial point (1000, 450)
p-450  = (-1/10)(x -1000)

-->   p = -x/10 +550

dumbcow · Answer

Revenue = price*quantity

---> x(-x/10 +550) = -x^2/10 + 550x

maximize revenue by setting derivative equal to 0

dumbcow · Answer

Profit = Revenue - Cost

maximize profit the same way

anonymous · Answer

Thanks

dumbcow · Answer

yw :)