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?

Answer 1

4000 bags of coffee

Explanation: see attached file

Answer 2

4000 bags

Step-by-step explanation:

Annual demand (D) = 36,000 bags

Set up cost(S) = $200

Holding cost (H) = $3.6

Production rate (p) = 200 bags per day

Demand rate (d) = D/number of days per year = 36000/240 = 150 bags per day

1) Optimum production quantity(Q) = √{2DS / H [1-(d/p)]}

= √{(2 x 36000 x 200) /3.6[1-(150/200)]}

= √{14400000/3.6(1-0.75)

= √ [14400000/(3.6 x 0.25)]

= √(14400000/0.09)

= √16000000

= 4000 bags