Assume that the technology of producing widgets is that every company entering the market has the same total cost curve, as follows:

TC=1000+5Q+0.1Q^2
Where : TC=Total cost per unit time
Q=Number of widgets produced per unit time

The market demand for widgets is:
Q=700-8P
Where P=price ($/widget)

a. What is the maximum number of firms that can survive in the market?
b. Suppose that, for whatsoever reason, there are only four firms in the market and, as noted above, they have identical cost curves. Assuming active price competition and no collusion among the firms, find the market supply function.
c. Given the assumptions and market supply function found in part b., above, find (i) the market price; (ii) the total quantity demanded; and (iii) the total cost, total revenue and profit for each firm.
d. Suppose that entry is attempted by a fifth firm, identical to the four firms already active in the market. Assuming that the fifth firm enters, find the new market supply curve.
e. Given the market supply curve of part d., above, find (i) the market price; (ii) the total quantity demanded; and (iii) the total cost, total revenue and profit for each firm.
f. What action could the original four firms take to prevent the entry of the fifth firm?