42. 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?
Question 42
Cost of labor = $100 per unit
Cost of capital = $400 per unit
Method 1 requires 50 units of labor and 10 units of capital
Total cost = [Units of labor * Cost per unit of labor] + [Units of capital * Cost per unit of capital]
Total cost = [50 * $100] + [10 * $400] = $5,000 + $4,000 = $9,000
The total cost of Method 1 is $9,000.
Method 2 requires 20 units of labor and 40 units of capital
Total cost = [Units of labor * Cost per unit of labor] + [Units of capital * Cost per unit of capital]
Total cost = [20 * $100] + [40 * $400] = $2,000 + $16,000 = $18,000
The total cost of Method 2 is $18,000.
Method 3 requires 10 units of labor and 70 units of capital
Total cost = [Units of labor * Cost per unit of labor] + [Units of capital * Cost per unit of capital]
Total cost = [10 * $100] + [70 * $400] = $1,000 + $28,000 = $29,000
The total cost of Method 3 is $29,000.
The company would incur the least cost using Method 1.
So,
The best production method is Method 1.
Now, the cost of labor rises to $200/unit.
Cost of labor = $200 per unit
Cost of capital = $400 per unit
Method 1 requires 50 units of labor and 10 units of capital
Total cost = [Units of labor * Cost per unit of labor] + [Units of capital * Cost per unit of capital]
Total cost = [50 * $200] + [10 * $400] = $10,000 + $4,000 = $14,000
The total cost of Method 1 is $14,000.
Method 2 requires 20 units of labor and 40 units of capital
Total cost = [Units of labor * Cost per unit of labor] + [Units of capital * Cost per unit of capital]
Total cost = [20 * $200] + [40 * $400] = $4,000 + $16,000 = $20,000
The total cost of Method 2 is $20,000.
Method 3 requires 10 units of labor and 70 units of capital
Total cost = [Units of labor * Cost per unit of labor] + [Units of capital * Cost per unit of capital]
Total cost = [10 * $200] + [70 * $400] = $2,000 + $28,000 = $30,000
The total cost of Method 3 is $30,000.
The company would incur the least cost using Method 1.
So,
The best production method is Method 1.
42. A small company that shovels sidewalks and driveways has 100 homes signed up for its services this winter. It can us...
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