Question

1. 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 $165 per setup. The equipment on which the book is produced has an annual production volume of 27,000 copies. Wilson has 250 working days per year, and the lead time for a production run is 17 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

	Formula	Given data:
		Annual Demand (D) (number of units)	7,700
		Price per unit (p)	$ 13.00
	20%*p	Holding cost per unit (Hc)	$ 2.60
		Production set-up cost (Sc)	$ 165.00
		Annual production capacity (AC)	27,000
		Number of days (n)	250
		Lead time (Lt) (in days)	17
	Formula	Calculations:
	D/n	Usage rate (U) (unit/day)	30.8
	AC/n	Production (P) (unit/day)	108
Ans (a)	[(2D*Sc/Hc)^0.5]*[(P/(P-U)]	Minimum cost production lot size (Q*)	1,169
Ans (b)	D/Q*	Number of production runs per year	6.59
Ans (c)	Q*/U	Cycle Time (in days)	37.96
Ans (d)	Q*/P	Length of a production run (in days)	10.83
Ans (e)	(Q*/P)*(P-U)	Maximum inventory (in number of units) (Imax)	836
Ans (f)	(Imax*Hc/2) + (D/Q*)*Sc	Total annual cost	2,173
Ans (g)	P/Lt	Reorder point	6