Question 1183174
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Marginal cost is the derivative of the Cost function, but since you are asking for the revenue function, the cost has no bearing.  Revenue is simply the price per unit times the quantity sold.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ R(q)\ =\ 210q]


given the unit price of 210.


On the other hand, if what you really wanted was a Profit function, then you need to determine the cost function.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ MC\ =\ \frac{dC}{dq}\ =\ 160]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ dC\ =\ 160dq]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \int\,dC\ =\ \int\,160\,dq]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ C(q)\ =\ 160q\ +\ C]


And the constant in this case is the fixed costs of 75,000,


So


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ C(q)\ =\ 160q\ +\ 75000]


Profit is then the difference between revenue and cost:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P(q)\ =\ R(q)\ -\ C(q)\ =\ 210q\ -\ (160q\,+\,75000)\ =\ 50q\ -\ 75000]


Extra credit:  How many units must the company make and sell in order to not lose money?

																
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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