Question

Hat Tricks Company (HTC) is a Buffalo, New York, manufacturer of hats and gloves. Recently, the company purchased a new machine to aid in producing the hat product lines. Production efficiency on the new machine increases with the workforce experience. It has been shown that as cumulative output on the new machine increases, average labor time per unit decreases up to the production of at least 3,200 units. As HTC’s cumulative output doubles from a base of 100 units produced, the cumulative average labor time per unit declines by a learning rate of 80%.

HTC has developed a new style of men’s hat to be produced on the new machine. One hundred of these hats can be produced in a total of 20 labor hours. All other direct costs to produce each hat are $19 per hat, excluding direct labor cost. Direct labor cost per hour is $60. Fixed costs are $8,000 per month, and HTC has the capacity to produce 3,200 hats per month.

Answer 1

The best production method is Method 1 with a total cost of $9,000. If the cost of labor rises to $200/unit, the company should still use Method 1 with a total cost of $14,000.

Step-by-step explanation:

Best Production Method:

The best production method can be determined by comparing the cost of labor and the cost of capital for each method. Method 1: 50 units of labor and 10 units of capital have a cost of $100/unit * 50 units of labor + $400/unit * 10 units of capital = $5,000 + $4,000 = $9,000. Method 2: 20 units of labor and 40 units of capital have a cost of $100/unit * 20 units of labor + $400/unit * 40 units of capital = $2,000 + $16,000 = $18,000. Method 3: 10 units of labor and 70 units of capital have a cost of $100/unit * 10 units of labor + $400/unit * 70 units of capital = $1,000 + $28,000 = $29,000.

Therefore, the best production method is Method 1 with a total cost of $9,000.

Rise in Labor Cost:

If the cost of labor rises to $200/unit, we can calculate the new costs for each method. Method 1: $200/unit * 50 units of labor + $400/unit * 10 units of capital = $10,000 + $4,000 = $14,000. Method 2: $200/unit * 20 units of labor + $400/unit * 40 units of capital = $4,000 + $16,000 = $20,000. Method 3: $200/unit * 10 units of labor + $400/unit * 70 units of capital = $2,000 + $28,000 = $30,000.

In this case, the company should use Method 1 even with the rise in labor cost because it still has the lowest total cost of $14,000.