A laptop manufacturer wants to compare the total cost of assembling its laptops in the United States versus Taiwan. All of the laptops will be sold in the United States. To evaluate inventory, it uses a safety factor of 2.25. The holding cost per laptop is $4 per week in the United States and $3.50 per week in Taiwan. The lead time with U. S. production is one week, whereas it is eight weeks with production in Taiwan. In addition, it costs $2 to ship laptops to the United States from Taiwan. Weekly demand is 1,000 laptops, with a standard deviation of 800.

a. What is the per-unit holding cost of a laptop with U. S. production?

b. What is the per-unit holding cost of a laptop with production in Taiwan?

c. A laptop requires 40 minutes of labor to assemble in the United States or in Taiwan. The total cost of labor in the United States is $40 per hour, while in Taiwan it is $10. What is the change in cost per laptop if it switches production to Taiwan?

a. The per-unit holding cost of a laptop with U. S. production is $16.724

b. The per-unit holding cost of a laptop with production in Taiwan is $51.625

c. The change in cost per laptop if it switches production to Taiwan is $16,891 per unit

Explanation:

a. According to the given data we have the following:

U. S. production on-order inventory is 1 * 1,000 = 1,000 units.

U. S. production on-hand inventory is sqrt (1 + 1) * 1,000 * 2.25 = 3,181 units.

To calculate the per-unit holding cost of a laptop with U. S. production we would have to use the following formula:

Average holding cost per unit with U. S. production=Average weekly holding cost/weekly demand

Total average inventory is 1,000 + 3,181 = 4,181 units.

Average weekly holding cost is $4 * 4,181 = $16,724.

Therefore, Average holding cost per unit with U. S. production = 16,724 / 1,000 = $16.724

b. According to the given data we have the following:

Taiwan on-order inventory production in is 8 * 1,000 = 8,000 units.

Taiwan on-hand inventory production is sqrt (8 + 1) * 1,000 * 2.25 = 6,750 units.

Total average inventory is 8,000 + 6,750 = 14,750

Average weekly holding cost is $3.5 * 14,750 = $51,625

Average holding cost per unit with production in Taiwan is 51,625 / 1,000 = $51.625

c. To calculate the change in cost per laptop if it switches production to Taiwan we would have to make the following calculations:

United States production stays, the labor cost per unit is $40 * 2/3 = $26.67.

There is no transportation cost, and the average holding cost per unit is $16.724

The total cost is 26.67 + 16.724 = $43.394 per unit.

Taiwan production, the labor cost per unit is $10 * 2/3 = $6.66

There is a $2 per unit transportation cost and an average holding cost per unit of $51.625

This is a total of 6.66 + 2 + 51.625 = $60.285 per unit.

Therefore, If production moves to Taiwan, the cost increases by 60.285 - 43.394 = $16.891 per unit.