Question

M. P. VanOyen Manufacturing has gone out on bid for a regulator component. Expected demand is 675 units per month. The item can be purchased from either Allen Manufacturing or Baker Manufacturing. Their price lists are shown in the table. Ordering cost is ​$45​, and annual holding cost per unit is ​$4.                                                                                      Allen Mfg. Baker Mfg. Quantity Unit Price Quantity Unit Price ​1-499 ​$16.00   ​1-399 ​$16.10   ​500-999 15.50 ​400-799 15.60 ​1000+ 15.00 ​800+ 15.10 ​​c) What is the optimal order quantity and total annual cost of​ ordering, purchasing, and holding the​ component? The optimal order quantity is _____ with a total cost of ​$ ______ ​(round your responses to the nearest whole​ number).

Answer 1

Annual demand = 675*12= 8100= D
EOQ = Square root ((2*D*S)/h) S = ordering cost per order = $45 and h = holding cost per unit per year= $4
EOQ = Sqrt((2*8100*45)/4) = 426.91 = 427 (Rounded to nearest whole number)

For Allen Manufacturing,

For Quantity 1-499,

Feasible quantity = 427 = EOQ

Total cost at EOQ 427 = (8100/427)*45 + (427/2)*4 +8100*16 = 131307.63

For Quantity 500-999,

Feasible quantity = 500 = EOQ

Total cost at Quantity 500 = (8100/500)*45 + (500/2)*4 +8100*15.5 = 127279

For Quantity 1000+,

Feasible quantity = 1000 = EOQ

Total cost at Quantity 1000 = (8100/1000)*45 + (1000/2)*4 +8100*15 `= 123864.5

Baker Manufacturing,

For Quantity 1-399,

Feasible quantity = 427 = EOQ

Total cost at EOQ 427 = (8100/427)*45 + (427/2)*4 +8100*16.1 = 132117.63

For Quantity 400-799,

Feasible quantity = 427

Total cost at EOQ 427 = (8100/427)*45 + (427/2)*4 +8100*15.6 = 128067.63

For Quantity 800+,

Feasible quantity = 800 = EOQ

Total cost at Quantity 800 = (8100/800)*45 + (800/2)*4 +8100*15.1= 124365.625

As we can see total cost is lowest for ordering quantity = 1000 for Allen manufacturing so that should be the supplier to be used

The optimal order quantity is 1000 with a total cost of ​$ 123865 (Rounded to nearest whole number)