Question

A coffee roaster in Richardson has opened a retail store adjacent to the production plant. The plant manager wishes to optimize the inventory costs of the company’s best-selling coffee. The annual demand for the coffee is 36,000 bags and the plant works 240 days per yr. The plant can roast the coffee at a rate of 200 bags per day. The cost to prepare the equipment to start a production run is $200 and the annual inventory carrying cost is $3.6 per year. 1. What should be the optimum quantity of coffee to produce? 2. What is the maximum inventory achieved during a production run? 3. How many production runs are needed to meet the annual demand? 4. What is the average inventory of coffee? 5. What is the total annual cost of producing and storing the company’s best-selling coffee?

Answer 1

1. 4,000 bags

2. 1,000

3. 180 runs

4. 18,000

5. $165,600

Step-by-step explanation:

1.

Q =
`√(2*D*S/C*(1-D/N/P))`

`√(2*36,000*200/3.6*(1-36,000/240/200))`

`√(16,000,000)`

= 4,000 bags

2.

Maximum Inventory = Q* (1 - D/N/P)

4,000*0.25

= 1,000

3.

Annual demand / Bags of coffee roasted per day

36,000 bags / 200 bags

= 180 runs

4.

Annual average inventory

36,000/2

=18,000

5.

Production Cost $200 * 180 runs = $36,000

Carrying Cost $3.6 * 36,000 bags = $129,600

Total Cost = $36,000 + $129,600

= $165,600