Question

For a certain company, the cost function for producing x items is C(x)=30x+200 and the revenue function for selling x items is R(x)=−0.5(x−70)2+2,450. The maximum capacity of the company is 110 items. The profit function P(x) is the revenue function R(x) minus the cost function C(x). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit! 1.Assuming that the company sells all that it produces, what is the profit function? P(x)= . Hint: Profit = Revenue - Cost. 2.What is the domain of P(x)? Hint: Does calculating P(x) make sense when x=−10 or x=1,000? 3.The company can choose to produce either 40 or 50 items. What is their profit for each case, and which level of production should they choose? Profit when producing 40 items = Profit when producing 50 items = 4.Can you explain, from our model, why the company makes less profit when producing 10 more units?

          For a certain company, the cost function for producing x items
is C(x)=30x+200 and the revenue function for selling x items is
R(x)=−0.5(x−70)2+2,450. The maximum capacity of the company is 110
items. The profit function P(x) is the revenue function R(x) minus the cost function C(x). In economic models, one typically assumes that a company
wants to maximize its profit, or at least make a profit!

1.Assuming that the company sells all that it produces, what is
the profit function? P(x)= . Hint: Profit
= Revenue - Cost.
2.What is the domain of P(x)? Hint: Does calculating P(x) make
sense when x=−10 or x=1,000?
3.The company can choose to produce either 40 or 50 items. What
is their profit for each case, and which level of production should
they choose?
Profit when producing 40 items =
Profit when producing 50 items =
4.Can you explain, from our model, why the company makes less
profit when producing 10 more units?

Added by David M.

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