Question

Optimization Problem - Profit, please help!

Answer 1

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

Answer 2

not quadratic if that helps any

Answer 3

1000(450-10x) ?

Answer 4

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

Answer 5

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

Answer 6

nevermind that's wrong

Answer 7

@Mertsj @ganeshie8 any idea on part A ?

Answer 8

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

Answer 9

Revenue = price*quantity

---> x(-x/10 +550) = -x^2/10 + 550x

maximize revenue by setting derivative equal to 0

Answer 10

Profit = Revenue - Cost

maximize profit the same way

Answer 11

Thanks

Answer 12

yw :)