Final answer:
The best production method is determined by evaluating the costs of labor and capital for each method. Method 1 is the most cost-effective initially and remains so even if labor costs increase or if the cost of capital decreases.
Step-by-step explanation:
When evaluating the best production method, we must consider the costs of labor and capital for each method. With labor costing $100/unit and capital costing $400/unit:
- Method 1 incurs a cost of (50 units of labor × $100/unit) + (10 units of capital × $400/unit) = $5,000 + $4,000 = $9,000.
- Method 2 incurs a cost of (20 units of labor × $100/unit) + (40 units of capital × $400/unit) = $2,000 + $16,000 = $18,000.
- Method 3 incurs a cost of (10 units of labor × $100/unit) + (70 units of capital × $400/unit) = $1,000 + $28,000 = $29,000.
Thus, Method 1 is the most cost-effective initially. If the cost of labor rises to $200/unit, the costs change:
- Method 1: ($200 × 50) + ($400 × 10) = $14,000.
- Method 2: ($200 × 20) + ($400 × 40) = $18,000.
- Method 3: ($200 × 10) + ($400 × 70) = $30,000.
Even with increased labor costs, Method 1 remains the least expensive. Finally, if the cost of labor remains at $40/unit, but the cost of capital decreases to $50/unit, the total cost for each method would be:
- Method 1: ($40 × 50) + ($50 × 10) = $2,000 + $500 = $2,500.
- Method 2: ($40 × 20) + ($50 × 40) = $800 + $2,000 = $2,800.
- Method 3: ($40 × 10) + ($50 × 70) = $400 + $3,500 = $3,900.
In this last scenario, Method 1 should be used as it is still the most cost-effective.