QUICK help for medal?

Question

anonymous · Answer

A manufacturer has been selling 1000 television sets a week at $450 each.  A market survey indicates that for each $10 rebate offered to the buyer, the number of sets sold will increase by 100 per week.

I know the demand function is y= 10x +1000
y=number of tvs sold
x=the amount of rebate

What I need to know is...How large a rebate should the company offer the buyer in order to maximize its revenue?

anonymous · Answer

I've looked all over the place, but no one can give a clear answer

anonymous · Answer

I'd appreciate it

anonymous · Answer

we can do this give me a second

anonymous · Answer

we are going to have to find the vertex of a quadratic equation

anonymous · Answer

i have no idea what a "demand" function is, but lets work slow
if there is no rebate he sells 1000 at 450 for a total of 450000
if he gives one rebate of $10 he sells $1000+100$ tvs at $450-100$ each for a total of $$(1000+10)(450-10)$$

anonymous · Answer

if he  gives two rebates he sells $1000+200$ tvs for $450-2\times 10$ for a total of $(1000+100\times 2)(450-10\times 2)$

anonymous · Answer

and more generally if he gives $x$ rebates he sells $$1000+100x$$ tvs for $$450-10x$$ dollars for a total of $$(1000+100x)(450-10x)$$ dollars

anonymous · Answer

expand, get a quadratic with negative leading coefficient that opens down, find the vertex which will give you the optimal number of rebates as $x$ and the amount made as \*y\)