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?

To answer these questions, we need to calculate a few parameters. Let's go step by step:

a) To determine how many scissors Jan should produce in each batch, we need to find the economic production quantity (EPQ). The formula for EPQ is:

EPQ = √((2DS)/H)

Where D is the annual demand, S is the setup cost, and H is the holding cost per unit per year.

Using the given values, D = 9000, S = $125, and H = $0.55, we can plug these values into the formula:

EPQ = √((2*9000*125)/0.55)
= √(2250000/0.55)
= √4090909.09
≈ 2022

Therefore, Jan should produce approximately 2022 scissors in each batch.

b) To find the maximum inventory, we need to multiply the production batch size (EPQ) by the number of days between batches. In this case, we assume Jan produces scissors continuously without any inventory buildup, so the number of days between batches is simply 0. Thus, the maximum inventory is:

Maximum inventory = EPQ * 0
= 0

Therefore, the maximum inventory is zero.

c) The average inventory can be found using the formula:

Average inventory = (EPQ/2)

Substituting the value of EPQ we calculated earlier:

Average inventory = 2022/2
= 1011

So, the average inventory is 1011 scissors.

d) The number of production runs in a year can be determined by dividing the annual demand by the production batch size:

Production runs per year = Annual demand / EPQ
= 9000 / 2022
≈ 4.45

Therefore, Jan will make approximately 4 to 5 production runs in a year.

e) The annual setup cost is calculated by multiplying the number of production runs by the setup cost:

Annual setup cost = Production runs per year * Setup cost
= 4.45 * 125
≈ $556.25

So, the annual setup cost is approximately $556.25.

f) The annual holding cost can be found by multiplying the average inventory by the holding cost per unit per year:

Annual holding cost = Average inventory * Holding cost
= 1011 * $0.55
≈ $556.05

Therefore, the annual holding cost is approximately $556.05.

g) The total inventory cost is the sum of the annual setup cost and the annual holding cost:

Total inventory cost = Annual setup cost + Annual holding cost
≈ $556.25 + $556.05
≈ $1112.30

Thus, the total inventory cost is approximately $1112.30.

a) To determine how many scissors Jan should produce in each batch, we need to consider the demand and the production rate. Jan produces 185 scissors per day on average, and the demand is 45 scissors per day.

Dividing the demand by the production rate will give us the batch size:

Batch size = Demand / Production rate
Batch size = 45 scissors per day / 185 scissors per day

Using a calculator or performing the division, we find that the batch size is approximately 0.243 or 0.24 (rounded to two decimal places).

Therefore, Jan should produce approximately 0.24 batches per day. Since it is not possible to produce a fraction of a batch, Jan should produce 1 batch of scissors per day.

b) The maximum inventory would occur when the production rate matches the demand rate, which is 45 scissors per day. Since Jan produces 185 scissors per day, the maximum inventory would be:

Maximum Inventory = Production rate - Demand rate
Maximum Inventory = 185 scissors per day - 45 scissors per day

Using a calculator or performing the subtraction, we find that the maximum inventory is 140 scissors.

c) The average inventory can be calculated by dividing the maximum inventory by 2:

Average Inventory = Maximum Inventory / 2
Average Inventory = 140 scissors / 2

Using a calculator or performing the division, we find that the average inventory is 70 scissors.

d) The number of production runs made each year can be calculated by dividing the total demand by the batch size:

Number of Production Runs = Total Demand / Batch Size
Number of Production Runs = 9,000 scissors / 1 batch

Using a calculator or performing the division, we find that the number of production runs is 9,000.

e) The annual setup cost is determined 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 = 9,000 * $125

Using a calculator or performing the multiplication, we find that the annual setup cost is $1,125,000.

f) The annual holding cost can be 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 pair
Annual Holding Cost = 70 scissors * $0.55

Using a calculator or performing the multiplication, we find that the annual holding cost is $38.50.

g) The total inventory cost is the sum of the annual setup cost and the annual holding cost:

Total Inventory Cost = Annual Setup Cost + Annual Holding Cost
Total Inventory Cost = $1,125,000 + $38.50

Using a calculator or performing the addition, we find that the total inventory cost is $1,125,038.50.