For a certain company, the cost function for producingxitems isC(x)=40x+200and the revenue function for sellingxitems isR(x)=0.5(x110)^2+6,050. The maximum capacity of the company is130items.

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

P(x)=

Hint: Profit = Revenue - Cost as we examined in Discussion 3.

What is the domain ofP(x)

Hint: Does calculatingP(x) make sense whenx=10 orx=1,000?

The company can choose to produce either70 or80 items. What is their profit for each case, and which level of production should they choose?

Profit when producing70 items =

Profit when producing80 items =

Can you explain, from our model, whythe company makes less profitwhen producing 10 more units?