Question

Wilson Publishing Company produces books for the retail market. Demand for a current book is expected to occur at a constant annual rate of 7,700 copies. The cost of one copy of the book is $13. The holding cost is based on an 20% annual rate, and production setup costs are $170 per setup. The equipment on which the book is produced has an annual production volume of 22,500 copies. Wilson has 250 working days per year, and the lead time for a production run is 12 days. Use the production lot size model to compute the following values:

1. Minimum cost production lot size. Round your answer to the nearest whole number. Do not round intermediate values.
   
   Q^* =   
   
2. Number of production runs per year. Round your answer to two decimal places. Do not round intermediate values.
   
   Number of production runs per year =   
   
3. Cycle time. Round your answer to two decimal places. Do not round intermediate values.
   
   T =   days
   
4. Length of a production run. Round your answer to two decimal places. Do not round intermediate values.
   
   Production run length =   days
   
5. Maximum inventory. Round your answer to the nearest whole number. Do not round intermediate values.
   
   Maximum inventory =   
   
6. Total annual cost. Round your answer to the nearest dollar. Do not round intermediate values.
   
   Total annual cost = $    
   
7. Reorder point. Round your answer to the nearest whole number. Do not round intermediate values.
   
   r =  

Answer 1

Given values:

Annual demand (D) = 7700 copies

Cost of the book (C) = $13

Holding cost (H) = 20% of cost of book = 20% of $13

Holding cost (H) = $2.6

Setup costs (S) = $170

Annual production volume = 22500 copies

Number of working days = 250

Lead time (L) = 12 days

Daily demand (d) = Annual demand / Number of working days = 7700 / 250

Daily demand (d) = 30.8 copies

Daily production (p) = Annual production / Number of working days = 22500 / 250

Daily production (p) = 90 copies

(a) Minimum cost production lot size (Q):

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

Q = SQRT [(2 x 7700 x $170) / $2.6 x (1 - 30.8/100)]

Q = 1,206.27

Minimum cost production lot size (Q) = 1,206.27 copies

(b) Number of production runs:

Number of production runs = Annual demand (D) / Production quantity (Q)

Number of production runs = (7,700 / 1,206.27)

Number of production runs = 6.38 runs per year

(c) Cycle time:

Cycle time = Production quantity (Q) / Daily demand (d)

Cycle time = 1,206.27 / 30.8

Cycle time = 39.16 days

(d) Length of a production run:

Length of production run = Production quantity (Q) / Daily production (p)

Length of production run = 1,206.27 / 90

Length of production run = 13.40 days

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