Question: For a certain company, the cost function for producingx items isC(x)=30x+150 and the revenue function for sellingx items isR(x)=0.5(x100)^2+5,000 The maximum capacity of the company

For a certain company, the cost function for producingx items isC(x)=30x+150

and the revenue function for sellingx items isR(x)=0.5(x100)^2+5,000

The maximum capacity of the company is140

items.

1.What is the domain ofP(x)

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

2.The company can choose to produce either70

or80items. What is their profit for each case, and which level of production should they choose?

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

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