Answer:
Quantity = 59 units
Price = $111
Step-by-step explanation:
The Demand function is given by
![P = 170 - Q](https://tex.z-dn.net/?f=P%20%3D%20170%20-%20Q)
The Marginal cost is given by
![MC = 52](https://tex.z-dn.net/?f=MC%20%3D%2052)
We are asked to find the quantity and price of goods.
Firstly, obtain the Marginal revenue function from the demand function
The Total revenue is given by
![TR = P \times Q \\\\TR = (170 - Q) \times Q \\\\TR = 170Q - Q^2](https://tex.z-dn.net/?f=TR%20%3D%20P%20%5Ctimes%20Q%20%5C%5C%5C%5CTR%20%3D%20%28170%20-%20Q%29%20%5Ctimes%20Q%20%5C%5C%5C%5CTR%20%3D%20170Q%20-%20Q%5E2)
The Marginal revenue is the derivative of the Total revenue,
![MR = \frac{d}{dQ} (TR) = 170Q - Q^2 \\\\MR = \frac{d}{dQ} (TR) = 170 - 2Q \\\\](https://tex.z-dn.net/?f=MR%20%3D%20%5Cfrac%7Bd%7D%7BdQ%7D%20%28TR%29%20%3D%20170Q%20-%20Q%5E2%20%5C%5C%5C%5CMR%20%3D%20%5Cfrac%7Bd%7D%7BdQ%7D%20%28TR%29%20%3D%20170%20-%202Q%20%5C%5C%5C%5C)
Assuming that the monopolist maximizes profits,
![MR = MC \\\\170 - 2Q = 52\\\\2Q = 170 - 52\\\\2Q = 118\\\\Q = 118/2\\\\Q = 59](https://tex.z-dn.net/?f=MR%20%3D%20MC%20%5C%5C%5C%5C170%20-%202Q%20%3D%2052%5C%5C%5C%5C2Q%20%3D%20170%20-%2052%5C%5C%5C%5C2Q%20%3D%20118%5C%5C%5C%5CQ%20%3D%20118%2F2%5C%5C%5C%5CQ%20%3D%2059)
Therefore, the quantity is 59 units.
The price of each good is
![P = 170 - Q \\\\P = 170 - 59 \\\\P = 111](https://tex.z-dn.net/?f=P%20%3D%20170%20-%20Q%20%5C%5C%5C%5CP%20%3D%20170%20-%2059%20%5C%5C%5C%5CP%20%3D%20111)
Therefore, the price is $111.
The answer is -3x^2+10xy+8y^2
Answer:
EASY PEASY
Step-by-step explanation:
9²
HOPE IT HELPS YOU
25-3=22
22/2 = 11
John made 14 free throws while Jose made 11.