One urgent question :)

I'll be perfectly honest, I've never done this type of question before. However, I think I did it right.

Begin by sketching a graph of units sold against price. As it's linear, it's going to be a straight line, crossing the y (units) axis at 140 (when £=0) and the x (price) axis at 70 (when units sold = 0).



The gradient of this line is $\frac{\Delta y}{\Delta x}=\frac{-140}{70}=-2$. So, from the equation of a straight line, using the point (70,0), $y=-2(x-70)=-2x+140$.

We want to maximise units x price, that is xy. $xy=x(-2x+140)=-2x^2+140x$.

This is maximised when its derivative is 0: $\frac{d(xy)}{dx}=-4x+140=0$, that is when x=35. This can also be found by completing the square, with no calculus:

$-2x^2+140x=-2(x^2-70x)=-2((x-35)^2-35^2)$ which has a turning point when x=35.

This answer is also what I would intuitively have gone for from the start. Don't put too much reliance on my guessing though - I may be completely wrong.

Someone please help me with this question. URGENT! I need to know how to do these types of questions. Thanks heaps

Adele makes hats and faces a linear demand curve for these hats. When she gives them away for free at the markets, 140 hats are taken. When she doesn't give them away for free, she finds that she has to keep prices below $70 to get any sales at all. What price will maximise Adele's revenue from the sale of hats?