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1. Assuming that the company sells all that it produces, what is the profit function?

2. What is the domain of P(x) ?

3. The company can choose to produce either 50 or 60 items. What is their profit for each case, and which level of production should they choose? Profit when producing 50 items? Profit when producing 60 items?

4. Can you explain, from our model, why the company makes less profit when producing 10 more units?

1 Assuming That The Company Sells All That It Produces What Is The Profit Function 2 What Is The Domain Of Px 3 The Company Can Choose To Produce Either 50 Or 6 class=

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Martebiidn

The  profit function is R(x) = -0.5 (x - 50²) + 1150

  • The domain of P(x)  is:  0 ≤ x ≤ 150
  • Profit when producing 50 items = 1150
  • Profit when producing 60 items =  1100

What is the profit function about?

Note that:

1. Profit  = Revenue - cost

P (x) =  0.5 ( x - 90²) + 4050 - 40x - 100  

= 0.5 ( x² - 180 + 8100 + 4050 - 40x - 100  

=0.5 x² - 50x - 100  

=0.5( x² - 100x) - 100  

=  -0.5 (x - 50²) + 1150

2.  Since the minimum unit is 50.

Then   x ≤ 150

X = describe the item so it need to be a negative number

  • x ≥ 0

Hence the domain of P(x)  is:  0 ≤ x ≤ 150

3. Assume x = 50 , 60

R(50) = 1150 , R (60 ) = -0.5 (60-50)² + 1150 = 1100

4. R (x) = -0.5 (x-50)² + 1150  then 50 more unit is removed hence, Profit when producing 60 items =  1100

Therefore, The  profit function is R(x) = -0.5 (x - 50²) + 1150

  • The domain of P(x)  is:  0 ≤ x ≤ 150
  • Profit when producing 50 items = 1150
  • Profit when producing 60 items =  1100

Learn more about profit function from

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