Hi

profit P(x),in thousands of dollars, for a firm when it sells x thousand units

 p(x)= -x^2+30x-50

a) What is the firm profit when it sells 1000 units: p(1) = 29-50 = -$21,000

b) What is the firms profit when it sells 10,000 units: p(10) = $150,000

c) how many units must the firm sell to break even: 1772 units

-x^2+30x-50 = -(x-15)^2 + 175

x = 1.77124, 28.22875

 


 
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation  (in our case ) has the following solutons:

  

  

  

  For these solutions to exist, the discriminant  should not be a negative number.

  

  First, we need to compute the discriminant : .

  

  Discriminant d=700 is greater than zero. That means that there are two solutions: .

  

    

    

    

    Quadratic expression  can be factored:

  

  Again, the answer is: 1.77124344467705, 28.228756555323.
Here's your graph:



  

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