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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 50 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 = -0.11x+242.
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(a) To answer question (a), simply substitute the value of x= 50 into the given formula
How much should be charged for the television set = -0.11*50 + 242 = 236.5.
(b) The revenue is this quadratic function
Revenue = p*x = (-0.11x+242)*x.
It has zeroes (x-intercepts) at x= 0 and x= = 2200.
The maximum of this quadratic function is at half-way between the x-intercepts,
which is = 2200/2 = 1100.
The maximum revenue is 1100*(-0.11*1100+242) = 133100.
(c) To answer question (c), simply substitute the value of x = = 1100 into the given formula
the price to charge in order to maximize revenue = -0.11*1100 + 242 = 121.
Solved in full.