2. William's Widgets is a widget manufacturer in the UK that owns two production facilities. At facility 1, widgets are produced according to the production function Q1 = 2L1, where Li denotes the number of worker hours at facility 1, and Q1 is the daily output of widgets at facility 1. Widgets at facility 2 are produced according to the production function Q2 = 312, where L2 denotes the number of worker hours at facility 2, and Q2 is the daily output of widgets at facility 2. (a) In terms of Li and L2, give an expression for William's total daily output of widgets. (5 points) (b) What is the marginal product of labor at each production facility? (5 points) Suppose that the two production facilities are located at opposite ends of the country; facility 1 is located in the north, while facility 2 is located down south. In the north workers can be hired at the hourly wage of wx - 10. Down south, workers can be hired at the hourly wage of ws = 20. You may assume that output can be freely transported at zero cost. (c) If the firm wants to produce 100 units of output at the lowest possible cost, how many worker-hours would the firm use at each production facility? (10 points) Now suppose the facilities are both located in the north (maintain the assumption that the hourly wage rate in the north is wa { 10). To operate properly, facility 1 requires William to spend f100 per day in maintenance, while facility 2 requires William to spend 2300 in maintenance. The maintenance fee at each facility can be avoided if William ceases operations (produces no output ) at that facility. (d) What is the total cost of producing @ units of output if William produces all @ units at facility 1? What is the total cost of producing Q units of output if William produces all Q units at facility 2? (10 points) (e) In terms of Q, what is the minimum total cost of producing Q units of output. (10 points)