Assuming that the function form of the short-term production cost of an enterprise is known under the condition of perfect competition: TC = 800 + 16q + Q^2 (q is the output), if the market price of the enterprise's products is $70, please calculate:

(1) What is the number of products produced to maximize the profit of the enterprise?

(2) What is the short-term equilibrium profit of the enterprise?

(3) According to the above calculation results, judge whether the enterprise should close down? Why?