SOLUTION: Can Someone please help me with this question The revenue, R, generated by selling games with a particular price is given by R(p) = �15p2 + 300 p + 1200. Graph the revenue functi

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Question 466677: Can Someone please help me with this question
The revenue, R, generated by selling games with a particular price is given by R(p) = �15p2 + 300 p + 1200. Graph the revenue function without a
calculator and find the price that
will yield the maximum revenue. What is the maximum revenue? Explain
in real world terms why this graph is parabolic.
Answer by ccs2011(207) (Show Source):
You can put this solution on YOUR website!
Revenue = price*quantity
Typically the higher the price the less likely someone will buy the product
Or in other words there is less demand
At a low price, quantity may be high but overall revenue will be low
As price increases, revenue increases
However, at some point the price will increase too much such that the quantity becomes too low and the overall revenue will start decreasing
This is the optimal price for maximum revenue.
At a very high price, quantity will be very low and revenue will be low as well
Thus the inverse relationship between price and quantity yields a parabolic revenue curve.
To find maximum, determine vertex of the graph.
Given quadratic equation of the form:

the x_coordinate of the vertex or line of symmetry is:

For our revenue function:
a = -15
b = 300
c = 1200

To find y_coordinate, substitute 10 into function

Vertex is at (10, 2700)
Thus max revenue is $2700 at a price of $10