Question

​Mac-in-the-Box, Inc., sells computer equipment by mail and telephone order. Mac sells

1,400

​flat-bed scanners per year. Ordering cost is

​$250,

and annual holding cost is

30

percent of the​ item's price. The scanner manufacturer offers the following price structure to​ Mac-in-the-Box:

                                                          

Order Quantity	Price per Unit
0 to 11	​$520
12 to 132	​$490
133 or more	​$450

The order quantity that minimizes total annual costs is

Answer 1

Question: Mac-in-the-Box, Inc., sells computer equipment by mail and telephone order. Mac sells 1,400 ​flat-bed scanners per year. Ordering cost is ​$250, and annual holding cost is 30 percent of the​ item's price. The scanner manufacturer offers the following price structure to​ Mac-in-the-Box:

Order Quantity	Price per unit
0 to 11	$520
12 to 132	$490
133 or more	$450

Answer: The order quantity that minimizes total annual cost is: "133 or more"

Explanation:

Given that;

Annual Demand (D) = 1400

Ordering Cost (S) = $250

Holding Cost (I) = 30%

Unit Cost (C) =

• Unit cost (0 to 11) = $520
• Unit cost (12 to 132) = $490
• Unit cost (133 to more) = $450  

Holding Cost (H) = I x C

• 30% x 520 = $156
• 30% x 490 = $147
• 30% x 450 = $135

Now, Economic Order Quantity is given by:

EOQ = (2 x D x S / H)1/2

Therefore:

If Unit cost = $520

EOQ = (2 x 1400 x 250 / 156)1/2

EOQ = (4487.18)1/2

EOQ = 66.99

The Total Annual Cost is given by:

Total Annual Cost (TAC) = (D x S) / EOQ + (EOQ x H) / 2

TAC = (1400 x 250) / 66.99 + (66.99 x 156) / 2

TAC = 10449.88

If Unit cost = $490

EOQ = (2 x 1400 x 250 / 147)1/2

EOQ = (4761.90)1/2

EOQ = 66.01

The Total Annual Cost is given by:

Total Annual Cost (TAC) = (D x S) / EOQ + (EOQ x H) / 2

TAC = (1400 x 250) / 66.01 + (66.01 x 147) / 2

TAC = 10143.96

If Unit cost = $450

EOQ = (2 x 1400 x 250 / 135)1/2

EOQ = (5185.19)1/2

EOQ = 72.01

The Total Annual Cost is given by:

Total Annual Cost (TAC) = (D x S) / EOQ + (EOQ x H) / 2

TAC = (1400 x 250) / 72.01 + (72.01 x 135) / 2

TAC = 9721.11

Hence, the order quantity which minimizes Total Annual Cost is "133 ro more", with respect to the Unit cost of $450, with Total Annual Cost of: $9721.11

Table:

Order Quantity	Price per unit	Total Annual Cost
0 to 11	$520	$10449.88
12 to 132	$490	$10143.96
133 or more	$450	$9721.11