The price p and the quantity x sold of a small flat-screen television set obeys the demand equation below.
a) how much should be charged for the television set if there are 70 television sets in stock?
b) what quantity x will maximize revenue? what is the maximum revenue?
c) what price should be charged in order to maximize revenue?
p= - 11 x+ 231

Ok... so, we know the price is
p = -11x + 231

a)
 
how much should be charged with only 70 sets?  70 is the quantity or "x"
thus  the price should be  p = -11(70) + 231  <-- because x = 70
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b)

first off, we need the Revenue function, or R(x)

revenue is flatly, how much you sold, at what price
we know the quantity is "x", we know the price is -11x+231
so R(x) is x*p  or  

R(x) = -11x²+231x

what quantity will maximize it? well, notice, is a quadratic with a negative leading term's coefficient, notice the picture below, anyhow, the graph uses Profit or P(x), but is the same case for R(x), they're both parabolic graphs opening downwards, and their vertex is the highest point, that is, maximum profit or revenue

so...  what's the vertex of R(x) = -11x²+231x ?

well  

so, the revenue is the maximum at 

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c)

what is "p" at that vertex? namely, what's the price at that maximum revenue?  well, is  

What mathematical statement is missing ? ? the answer is b