Question

For a certain company, the cost function for producing x items is C(x)=50x+150 and the revenue function for selling x items is R(x)=−0.5(x−100)2+5,000. The maximum capacity of the company is 140 items. The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost function C(x) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit! Assuming that the company sells all that it produces, what is the profit function? P(x)= . What is the domain of P(x)? The company can choose to produce either 50 or 60 items. What is their profit for each case, and which level of production should they choose? Profit when producing 50 items = Profit when producing 60 items = 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)=50x+150 and the revenue function for selling x items is
R(x)=−0.5(x−100)2+5,000. The maximum capacity of the company is 140
items. The profit function P(x) is the revenue function R(x) (how
much it takes in) minus the cost function C(x) (how much it
spends). In economic models, one typically assumes that a company
wants to maximize its profit, or at least make a profit! Assuming that the company sells all that it produces, what is
the profit function? P(x)= . What is the domain
of P(x)? The company can choose to produce either 50 or 60 items.
What is their profit for each case, and which level of production
should they choose? Profit when producing 50 items =  Profit
when producing 60 items =  Can you explain, from our model,
why the company makes less profit when producing 10 more units?

Added by Ray V.

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