Hi there, please answer these questions with full working out. Thanks

Q1) If the pre-tax cost function for John's Shoe Repair is C(q) = 100 + 10q - q² + 1/3q³ , and it faces a specific tax of t = 10, what condition determines the maximising output if the market price is p? Can you solve for a single, maximising q in terms of p?

Q2)Should a firm shut down (and why) if its revenue is R = $1,000 per week,

A) its variable cost is VC = $500, and its sunk fixed cost is F = $600?

B) its variable cost is VC = $1,001, and its sunk fixed cost F = $500?

Q3)Each of the 10 firms in a competitive market has a cost function of C = 25 + q² , so its marginal cost is MC = 2q . The market demand function is

Q = 120 - p . Determine the equilibrium price, quantity per firm, and market quantity.