# For a certain company, the cost function for producing x items is C(x)=50x+200 and the revenue function for selling x items is R(x)=−0

For a certain company, the cost function for producing x items is C(x)=50x+200 and the revenue function for selling x items is R(x)=−0.5(x−120)2+7,200. The maximum capacity of the company is 140 items. Part a : Answer the following questions about the cost function C(x) and the revenue function R(x). What is the domain and range of C(x)? Hint: Does calculating C(x) make sense when x=−10 or x=1,000? What is the meaning of the slope and intercept of C(x)? Hint: Review the Models and Applications reading from Module One. At what production level x will the company receive the most revenue? The maximum revenue occurs when x= . Hint: Look at the graph of a parabola. Part b : Answer the following questions about the profit function P(x). Assuming that the company sells all that it produces, what is the profit function? P(x)= . Hint: Profit = Revenue – Cost as we already discussed in Discussion 3. Why is finding the range of P(x) important? The company can choose to produce either 70 or 80 items. What is their profit for each case, and which level of production should they choose? Profit when producing 70 items = Profit when producing 80 items = Can you explain, from our model, why the company makes less profit when producing 10 more units?

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