Question 1203118
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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= {{{242/0.11}}} = 2200.

    The maximum of this quadratic function is at half-way between the x-intercepts,
    which is {{{x[optimum]}}} = 2200/2 = 1100.

    The maximum revenue is  1100*(-0.11*1100+242) = 133100.



(c)  To answer question (c), simply substitute the value of  x = {{{x[optimum]}}} = 1100 into the given formula

         the price to charge in order to maximize revenue = -0.11*1100 + 242 = 121.
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Solved in full.