For a certain company, the cost function for producing x items is C(x)=30x+150 and the revenue function for selling x items is R(x)=−0.5(x−110)2+6,050. The maximum capacity of the company is 160 items Assuming that the company sells all that it produces, what is the profit function?

P(x)=

What is the domain of P(x)?

The company can choose to produce either 80 or 90 items. What is their profit for each case, and which level of production should they choose?

Profit when producing 80 items =

Profit when producing 90 items =

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