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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(x90)2+4,050.
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Question

Please help me resolve this problem !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−90)2+4,050.

The maximum capacity of the company is 150 items.

Part a: Answer the following questions about the cost function C(x)

 and the revenue function R(x)

1-What is the domain and range of C(x)?

2-What is the meaning of the slope and intercept of C(x)?

3-At what production level x

 will the company receive the most revenue?

The maximum revenue occurs when x=?


Part b: Answer the following questions about the profit function P(x)

.

4-Assuming that the company sells all that it produces, what is the profit function? P(x)=

5-Why is finding the range of P(x) important?

6-The company can choose to produce either 60

 or 70 items. What is their profit for each case, and which level of production should they choose?

Profit when producing 60 items =

Profit when producing 70 items =

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

Step-by-step answer

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