Faye sells lemonade in a competitive market on a busy street corner in Philadelphia. His production function is (1, 2) = 1^1/32^1/3, where output is measured in gallons, 1 is number of pounds of lemons he uses, and 2 is the number of labor-hours spent squeezing them. 1 = $8 is the cost of a pound of lemons and 2 = $1 is the wage rate for lemon-squeezers. a) At the cost minimizing input bundle, how much labor-hours are spent per pound of lemons? That is, compute the rate of x2/x1 at the cost minimizing input bundle.

b) What are the optimal inputs bundle to produce 8 units of output in the cheapest way? c) What is the minimized cost of producing 8 units of output? d) Calculate the average cost when total cost of production is minimized and output is 8 units. e) If market price of output is $10 per unit (p=$10), conditional on firm is now producing 8 units of output in the cheapest way, what is firm's total profit? Determine firm's supply decision in long run.