3. There are 70 buyers of product \( X \) in the market. Assume each buyer has the same demand function that takes the form of \( P=280-\frac{70}{4} Q \). There is only one firm that produces product X and it has the follwoing cost functions:
\[
\begin{array}{l}
T V C=\frac{1}{6} Q^{2}+30 Q \\
T F C=15,000
\end{array}
\]
DR. NGUYEN ANH PHUONG
a. Identify the market's demand function.
b. Identify the functions for MC and MR.
c. Find the profit-maximising quantity and its respective price. What is the firm's maximum profit?
d. If there is a fixed tax of 10,000 imposed on the firm, will the firm change its production quantity? What is the total profit?
e. If the government impose a tax of 20/unit, what will the firm's price and production quantity be? What is the total profit?
f. In order to maximise production quantity without incurring loss, how many products should the firm produce and what is the price for each product?
g. If the maximum price the firm can sell is 172 , how many product will the firm produce to maximise its profit? Find the maximum profit.
