Question

Problem 14-13 (Algorithmic)

Wilson Publishing Company produces books for the retail market.
Demand for a current book is expected to occur at a constant
**annual rate of 6900 copies**. The **cost of
one copy of the book is $14.50**. The holding cost is based
on an **15% annual rate**, and production setup costs
are **$160 per setup**. The equipment on which the
book is produced has an **annual production volume of 21500
copies**. Wilson has 250 working days per year, and the lead
time for a **production run is 14 days**. Use the
production lot size model to compute the following values:

a) Minimum cost production lot size. Do not round intermediate values and round your final answer to two decimal places.

Q* =

b) Number of production runs per year. Do not round intermediate values and round your final answer to two decimal places.

Number of production runs per year =

c) Cycle time. Do not round intermediate values and round your final answer to two decimal places.

T = ___ days

d) Length of a production run. Do not round intermediate values and round your final answer to two decimal places.

Production run length = ___ days

e) Maximum inventory. Do not round intermediate values and round your final answer to two decimal places.

Maximum inventory =

f) Total annual cost. Do not round intermediate values and round your final answer to two decimal places.

Total cost = $

g) Reorder point. Do not round intermediate values and round your final answer to two decimal places.

r =

Answer #1

a) Optimum Lot Size =

here, A= annual demand, S = setup cost, H = holding cost @ of 15% of production cost.

optimum lot size= = 1007.56 copies.

b) no. of production runs = annual demand/ optimal lot size = 6900/1007.56 = 6.85 runs

c) cycle time :

no. of units in 1 production run that can be produced= 21500/6.85 = 3138.69 units

lead time for 3138.69 units = 14 days

lead time for 1007.56 units = 14*1007.56/3138.69 = 4.49 days.

f) total cost = optimal production size*cost of production*no of runs + set up cost*no of runs + holding cost * no of order = 1007.56*14.5*6.85 + 160*6.85 + 2.175*6.85 = $101186.80

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