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A mail-order house uses 18,000 boxes a year. Carrying costs are 60 cents per box a year, and ordering costs are $96 Answer

A mail-order house uses 18,000 boxes a year. Carrying costs are 60 cents per box a year, and ordering costs are $96. The following price schedule applies. Determine


 

Ans:

   

  

Price Level:  

1 

2 

3 

4 

Minimum quantity for price 

Qmin =

1000 

2000 

5000 

10000 

Price 

  

  

P = 

1.25 

1.20 

1.15 

1.10 

Optimal Q (for each price) 

Qopt =

2400 

2400 

5000 

10000 

Number of orders per year

D/Qopt =

7.5 

7.5 

3.6 

1.8 

Average Inventory 

 

Qopt/2 =

1200 

1200 

2500 

5000 

Annual carrying cost 

 

(Qopt/2) * H =

720 

720 

1500 

3000 

Annual ordering cost 

(D/Qopt) * S =

720 

720 

345.6 

172.8 

Annual purchase cost 

P * D = 

22500 

21600 

20700 

19800

Total Annual Cost 

  

TC = 

23940 

23040 

22545.6 

22972.8 

 

Annual Demand 

  

D = 

18000 

Ordering cost per order 

S = 

96 

Annual carrying cost per unit:  

H (fixed) = 

0.6 

 

1 

TRUE 

 

H (% of price) = 

  

Optimal Q (overall) 

  

Qopt =

5000 

         

Actual Order Quantity

Q = 

5000 

Increment 

  

Q =

10 

Price 

  

  

P = 

1.15 

Number of orders per year 

D/Q = 

3.6 

Average Inventory 

 

Q/2 = 

2500 

Annual carrying cost 

 

(Q/2) * H = 

1500 

Annual ordering cost 

(D/Q) * S = 

345.6 

Annual purchase cost 

P * D = 

20700 

Total Annual Cost

  

TC = 

22545.6 

 

a.The optimal order quantity.

Ans:

Optimal order quantity = 5000

b.The number of orders per year.

Ans: Number of orders per year = 3.6

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