$1)(35$ points$)$ An industry in the U$.$S$.$ is perfectly competitive, and each producer has a cost curve given by c$($q$)=72+5$q $+(1/4)$q$^2.$ In the short$-$run there are $20$ identical producers. The market demand curve is qd $=4755$p a$)$ What is the fixed cost? Write the expressions for average total cost, average variable cost, and marginal cost. b$)$ What would be the shutdown price for each firm in the short$-$run? What is the short$-$run market equilibrium in this industry $($assuming the fixed cost in the short run is not avoidable$)?$ c$)$ Represent demand and short$-$run supply in a market level diagram. d$)$ Compute the firm$$s profit. e$)$ Now, there is free entry and exit and all costs can be avoidable. What is the long$-$run equilibrium price in this industry, and at this price, how much would an individual firm produce? f$)$ Represent demand and long$-$run supply in a market level diagram. g$)$ How many active producers are in this industry in a long$-$run competitive market? How many producers entry in this industry? What is the total quantity produced in this industry?