A small company that shovels sidewalks and driveways has 100 homes signed up for its services this winter. It can use various combinations of capital and labor: intensive labor with hand shovels, less labor with snow blowers, and still less labor with a pickup truck that has a snowplow on front. To summarize, the method choices are:
Method 1: 50 units of labor, 10 units of capital
Method $2 : 20$ units of labor, 40 units of capital
Method $3 : 10$ units of labor, 70 units of capital
If hiring labor for the winter costs $\$ 100 /$ unit and a unit of capital costs $\$ 400,$ what is the best production method? What method should the company use if the cost of labor rises to $\$ 200 /$ unit?