Final answer:
The best production method is Method 2 with a total cost of $18,000. If the cost of labor rises to $200 per unit, it would still be the most cost-effective option.
Step-by-step explanation:
To determine the best production method, we need to calculate the total cost for each method based on the cost of labor and capital.
Using Method 1, the total cost would be $100 per unit of labor times 50 units, plus $400 per unit of capital times 10 units, which equals $5,000 + $4,000 = $9,000.
Similarly, for Method 2, the total cost would be $100 per unit of labor times 20 units, plus $400 per unit of capital times 40 units, which equals $2,000 + $16,000 = $18,000.
Lastly, for Method 3, the total cost would be $100 per unit of labor times 10 units, plus $400 per unit of capital times 70 units, which equals $1,000 + $28,000 = $29,000.
Therefore, based on the cost of labor and capital, the best production method is Method 2 with a total cost of $18,000. If the cost of labor rises to $200 per unit, the new total cost for Method 2 would be $4,000 + $16,000 = $20,000, which is still the most cost-effective option.