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

Given:
Demand rate = 45 scissors per day
Production rate = 185 scissors per day

To find the batch size, we need to calculate the difference between the production rate and the demand rate:

Batch size = Production rate - Demand rate
Batch size = 185 - 45
Batch size = 140 scissors

Therefore, Jan should produce 140 scissors in each batch.

b) To find the maximum inventory, we need to consider the batch size and the demand rate. Assuming Jan produces the entire batch at the start, the maximum inventory is equal to the batch size.

Maximum inventory = Batch size
Maximum inventory = 140 scissors

Therefore, the maximum inventory would be 140 scissors.

c) To find the average inventory, we need to consider the batch size and the demand rate.

Average inventory = Batch size / 2
Average inventory = 140 / 2
Average inventory = 70 scissors

Therefore, the average inventory would be 70 scissors.

d) To calculate the number of production runs made each year, we need to divide the annual demand by the batch size.

Number of production runs = Annual demand / Batch size
Number of production runs = 9,000 / 140
Number of production runs ≈ 64.29

Since Jan cannot make fractional production runs, he would make 64 production runs each year.

e) The annual setup cost is calculated by multiplying the number of production runs by the cost to set up the production process.

Annual setup cost = Number of production runs * Setup cost
Annual setup cost = 64 * $125
Annual setup cost = $8,000

Therefore, the annual setup cost would be $8,000.

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

Annual holding cost = Average inventory * Holding cost per scissors
Annual holding cost = 70 * $0.55
Annual holding cost = $38.50

Therefore, the annual holding cost would be $38.50.

g) The total inventory cost is calculated by summing the annual setup cost and the annual holding cost.

Total inventory cost = Annual setup cost + Annual holding cost
Total inventory cost = $8,000 + $38.50
Total inventory cost ≈ $8,038.50

Therefore, the total inventory cost would be approximately $8,038.50.