Jan Gentry is the owner of a small company that pro¬duces electric scissors used to cut fabric. The annual demand is for 9,000 scissors and Jan produces the scissors in batches. On average, Jan can produce 185 scissors per day. Demand for scissors has been about 45 scis¬sors per day. The cost to set up the production process is $125, and it costs Jan 55 cents to carry one pair of scissors for one year.

a) How many scissors should Jan produce in each batch?

b) What will be the maximum inventory?

c) What will be the average inventory ?

d) How many production runs will be made each year?

e) What will the annual setup cost?

f) What will be the annual holding cost?

g) What will be the total inventory cost?

a 40

a) To determine how many scissors Jan should produce in each batch, we need to consider the annual demand for scissors and the production rate.

The annual demand is 9,000 scissors and the production rate is 185 scissors per day.

To calculate the number of scissors Jan should produce in each batch, we can divide the annual demand by the production rate:

Number of scissors in each batch = Annual demand / Production rate
= 9,000 scissors / 185 scissors per day
≈ 48.65 scissors

Since Jan cannot produce a fraction of a scissor, she should round up to the nearest whole number. Therefore, Jan should produce approximately 49 scissors in each batch.

b) The maximum inventory occurs when Jan produces a new batch before completely depleting the previous batch.

To calculate the maximum inventory, we need to find the time it takes to produce a batch and the daily demand.

Time to produce a batch = Number of scissors in each batch / Production rate
= 49 scissors / 185 scissors per day
≈ 0.265 days

Maximum inventory = Daily demand × Time to produce a batch
= 45 scissors per day × 0.265 days
≈ 11.93 scissors

Since Jan cannot have a fraction of a scissor in inventory, the maximum inventory would be 12 scissors.

c) The average inventory is the average amount of inventory Jan holds during the year.

To calculate the average inventory, we need to calculate the average daily demand and subtract it from the daily production rate.

Average daily demand = Annual demand / Number of working days in a year
= 9,000 scissors / 365 days
≈ 24.66 scissors per day

Average inventory = (Production rate - Average daily demand) × Time to produce a batch
= (185 scissors per day - 24.66 scissors per day) × 0.265 days
≈ 42.24 scissors

Therefore, the average inventory would be approximately 42 scissors.

d) The number of production runs made each year can be calculated by dividing the annual demand by the number of scissors produced in each batch.

Number of production runs = Annual demand / Number of scissors in each batch
= 9,000 scissors / 49 scissors
≈ 183.67 runs

Since Jan cannot have a fraction of a production run, the number of production runs made each year would be 183 runs.

e) The annual setup cost is the cost to set up the production process for each production run multiplied by the number of production runs made in a year.

Annual setup cost = Setup cost per production run × Number of production runs
= $125 per run × 183 runs
= $22,875

Thus, the annual setup cost would be $22,875.

f) The annual holding cost is the cost to carry one pair of scissors for one year multiplied by the average inventory.

Annual holding cost = Cost to carry one pair of scissors for one year × Average inventory
= $0.55 per pair per year × 42 scissors
= $23.10

Therefore, the annual holding cost would be $23.10.

g) The total inventory cost includes both the annual setup cost and the annual holding cost.

Total inventory cost = Annual setup cost + Annual holding cost
= $22,875 + $23.10
= $22,898.10

Thus, the total inventory cost would be $22,898.10.