Problem 1. A firms sells hospital-grade disinfectant in a perfectly competitive market for $60 per gallon. The firm's unavoidable fixed costs are $1000 this month and the firm can produce up to 50 gallons per month. The marginal costs when producing Q gallons are MgC(Q) = 10 + 2Q for all Q between zero and 50. (1.1) Write a mathematical expression for total revenue TR(Q), average revenue AR(Q), total cost TC(Q), variable cost VC(Q), average fixed cost AFC(Q), average variable cost AVC(Q) and average total cost ATC(Q) as a function of quantity Q. (1.2) Use your favorite spreadsheet software to plot a graph of MgC(Q), AVC(Q), AFC(Q), ATC(Q), and AR(Q) for Q between zero and 50. (1.3) If the firm wanted to maximize total revenue, how many gallons of disinfect tant should it produce? What would be the profits? (1.4) What quantity should the firm produce in order to maximize profits? (1.5) At the profit-maximizing level of output, how do marginal revenue and marginal cost compare? (1.6) Suppose that unavoidable fixed costs suddenly double. How should the firm change production to account for this sudden increase in cost? (1.7) Suppose the marginal cost increases by $2 at every level of production. How should the firm alter production to account for this sudden increase in cost