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Sagot :
Step 1
Write the demand function equation
[tex]Q=-9p^2+4p\text{ + 1970}[/tex]Step 2:
To find the price and quantity which maximize the revenue
You will find the derivative of Q with respect to price
[tex]\begin{gathered} \frac{dQ}{dp}\text{ = -18p + 4} \\ -18p\text{ + 4 = 0} \\ 18p\text{ = 4} \\ p\text{ = }\frac{4}{18}\text{ = }\frac{2}{9} \end{gathered}[/tex]Step 3:
Find the quantity demand by substituting p = 2/9
[tex]\begin{gathered} Q\text{ = -9 }\times\text{ (}\frac{2}{9})^2\text{ + 4 }\times\text{ }\frac{2}{9}\text{ + 1970} \\ =\text{ -0.44 + 0.888 + 1970} \\ =\text{ 1970.444} \\ =\text{ 1970} \end{gathered}[/tex]Final answer
The price which maximizes the total revenue is p = 2/9
The quantity is Q = 1970
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