Question

An important mathematical application in economics is to model the cost and revenue for a company. Net profit that the company earns is the value remaining after all operating expenses are subtracted from the revenue. Thus, Profit = Revenue - Cost, that is, P(x) = R(x) - C(x). For this Discussion, suppose that for a certain company, the cost for producing items is 35x+300 and the revenue for selling items is 70x−0.5x2. Part a. What's the profit function, P(x) ? Part b. Show work to find two values of x that will earn a profit of $200. Part c. Is it possible for the company to earn a profit of $2,000? (Hint: What happen to the discriminant when P(x) = 2000? Will there be real solutions? Why or why not? Please show work! )

          An important mathematical application in economics is to model the cost and revenue for a company.  Net profit that the company earns is the value remaining after all operating expenses are subtracted from the revenue.  Thus, Profit = Revenue - Cost, that is, P(x) = R(x) - C(x).
For this Discussion, suppose that for a certain company, the cost for producing  items is 35x+300 and the revenue for selling  items is 70x−0.5x2.
Part a.  What's the profit function, P(x) ?
Part b.  Show work to find two values of x that will earn a profit of $200.
Part c.  Is it possible for the company to earn a profit of $2,000?  (Hint: What happen to the discriminant when P(x) = 2000?  Will there be real solutions?  Why or why not?  Please show work! )

Added by Rhonda F.

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