discussion question

Question

For a certain company, the cost function for producing x items is C(x)=30x+100 and the revenue function for selling x items is R(x)=−0.5(x−90)2+4,050 . The maximum capacity of the company is 140 items.

1. Assuming that the company sells all that it produces, what is the profit function?
2. P(x)=
3. What is the domain of P(x)?
4. Hint: Does calculating P(x) make sense when x=−10= or x=1,000?
5. The company can choose to produce either 60 or 70items. What is their profit for each case, and which level of production should they choose?
6. Profit when producing 60 items =   
7.  Profit when producing 70 items =  
8. Can you explain, from our model, why the company makes less profit when producing 10 more units?

 

Answer 1

P(x)=R(x)-C(x)=-.5(x-90)^2+4050 -(30x+100)

=-.5(x-90)^2+4050-30x-100

=-.5x^2 +90x-4050+4050-30x-100

=-.5x^2 +60x -100

0<x<140

P(60)=-1800+3600-100

= 1700

P(70)=2450+4200-100

=1650

max P=1700, when P'=0=-x+60

x=60, when MC=MR

for x>60 MC>MR reducing Profit