Please help?

Question 2. Firm Optimization Let's play hypothetical here. Immag'ine you're the founder of a quale factory and you are consid ering your company's long-run options for production. You can either build your factory in London, with access to the larger wizarding labor market, or in Hogsmeade with its wizardingspecic zon- ing and low rental costs. The production function is q = LaK", regardle of where the factory is located. Labor is in worker-hours and capital is in leather processing machines. Part 3) Find an exprusion for the rm's M RTS. Part b) Using whatever method you prefer, nd expressions for the cost minimizing levels of L and K and the rm's long-run cost function C(w,r, (i), all in terms of prices 11), 'r, and quantity (2. Part c) Assume that a = %, b = g, regardless of where you locate the plant. If the rm locates in Hogsmeade, the rm will have to pay a wage, to = $5, and a cost of capital of r = $10. If it locates the plant in London it would have to pay higher wages, w = $36, but the cost of capital would be lower, r = $9. Given the rm expects to produce 1000 units of output regardless of the location chosen, what are the cost minimizing L and K (it is ne to have fractional units of labor and capital) for each location, and in which city can the rm produce at the lowest cost