Question

*** Please show the work of the right answer. don't post excel work

the correct answer is C

Suppose that a plant manager has taken OM course, and so she uses economic batch sizes for production of a product. Suppose further that the setup cost is $50, the holding cost per unit per year is $10, the annual demand is 30,000 units, the firm operates (and experiences demand) 300 days per year, and the production rate per day is 1000 units. What will be the maximum inventory level that this product ever reaches? A) 577 B) 30 C) 519 D) 27,000 E) 58

Answer 1

Solution:

Setup cost (S) = $50

Annual holding cost (H) = $10

Annual demand (D) = 30,000 units

Number of working days in a year = 300 days

Daily production (p) = 1000 units

Daily demand (d) = Annual demand / Number of working days in a year

Daily demand (d) = 30,000 / 300 = 100 units

Economic production quantity (Q) is calculated as,

Q = SQRT [(2 x D x S) / H x (1 - d/p)]

Putting the given values in the above formula,

Q = SQRT [(2 x 30,000 x $50) / $10 x (1 - 100/1000)]

Q = 577.35 or 577 (Rounding off to the nearest whole number)

Economic production quantity (Q) = 577 units

Now, Maximum inventory (Imax) is calculated as,

Imax = Q x (1 - d/p)

Imax = 577 x (1 - 100/1000)

Imax = 519.3 or 519 (Rounding off to the nearest whole number)

Maximum inventory = 519 units