Tax Preparers Inc. works 250 days per year. The company uses adding machine tape at a rate of eight rolls per day. Usage is believed to be normally distributed with a standard deviation of three rolls during lead time. The cost of ordering the tape is $10 and holding costs are $0.30 per roll per year. Lead time is two days.

(a) Calculate the economic order quantity

(Round your answer to 1 decimal place, the tolerance is +/-0.1.)

(b) What reorder point will provide an order cycle service level of 97 percent?
tapes (Round up your answer to the nearest whole number.)

(c) How much safety stock must the company hold to have a 97 percent order-cycle service level?
units (Round your answer to 2 decimal places, the tolerance is +/-0.01.)

(d) What reorder point is needed to provide an order-cycle service level of 99 percent?
tapes (Round up your answer to the nearest whole number.)

(e) How much safety stock must the company hold to have a 99 percent order-cycle service level?
units (Round your answer to 2 decimal places, the tolerance is +/-0.01.)

To solve this problem, we can use the economic order quantity (EOQ) formula to calculate the optimal order quantity for the adding machine tape. The formula for EOQ is:

EOQ = sqrt((2 * demand * setup cost) / holding cost)

(a) Calculate the economic order quantity:

Given information:
- Demand (usage) per day = 8 rolls
- Setup cost = $10
- Holding cost per roll per year = $0.30
- Working days per year = 250

First, we need to calculate the annual demand:
Demand per year = demand per day * working days per year
Demand per year = 8 rolls/day * 250 days/year = 2000 rolls/year

Next, we can substitute the values into the EOQ formula:
EOQ = sqrt((2 * demand * setup cost) / holding cost)
EOQ = sqrt((2 * 2000 * 10) / 0.30)
EOQ = sqrt((40000 * 10) / 0.30)
EOQ = sqrt(400000 / 0.30)
EOQ = sqrt(1333333.333)
EOQ ≈ 1154.7

Therefore, the economic order quantity is approximately 1154.7 rolls.

(b) To calculate the reorder point for a 97 percent order cycle service level, we need to determine the lead time demand.

Lead time demand = demand per day * lead time
Lead time demand = 8 rolls/day * 2 days = 16 rolls

Reorder point = (demand per day * lead time) + safety stock
Reorder point = 16 + safety stock

Using the normal distribution, we need to find the z-score associated with a 97 percent service level. The z-score can be found using a standard normal distribution table. The value associated with 97 percent is approximately 1.88.

Reorder point = 16 + (1.88 * standard deviation)

Given standard deviation = 3 rolls, we can substitute the values:
Reorder point = 16 + (1.88 * 3)
Reorder point = 16 + 5.64
Reorder point ≈ 21.64

Therefore, the reorder point that will provide a 97 percent order cycle service level is approximately 22 rolls.

(c) To calculate the safety stock for a 97 percent order cycle service level, we subtract the reorder point from the mean demand.

Safety Stock = mean demand - reorder point
Safety Stock = demand per day * lead time - reorder point
Safety Stock = 8 * 2 - 21.64
Safety Stock = 16 - 21.64
Safety Stock ≈ -5.64

Since the safety stock cannot be negative, we round down to zero.

Therefore, the company does not need to hold any safety stock for a 97 percent order cycle service level.

(d) To calculate the reorder point for a 99 percent order cycle service level, we follow the same steps as in part (b), but use the z-score associated with a 99 percent service level.

The z-score associated with 99 percent is approximately 2.33.

Reorder point = 16 + (2.33 * 3)
Reorder point = 16 + 6.99
Reorder point ≈ 23.99

Therefore, the reorder point that will provide a 99 percent order cycle service level is approximately 24 rolls.

(e) To calculate the safety stock for a 99 percent order cycle service level, we follow the same steps as in part (c).

Safety Stock = 16 - 23.99
Safety Stock ≈ -7.99

Rounding down to zero, the company does not need to hold any safety stock for a 99 percent order cycle service level.

Please note that safety stock calculations assume normal distribution and constant demand, which may not necessarily be the case in real-world scenarios.

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