Question

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

Answer 1

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

brainly.com/question/16866047

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