Keith Shoe Stores carries a basic black men’s dress shoe that sells at an approx
ID: 2930130 • Letter: K
Question
Keith Shoe Stores carries a basic black men’s dress shoe that sells at an approximate constant rate of 500 pairs of shoes every three months. Keith’s current buying policy is to order 500 pairs each time an order is placed. It costs Keith $30 to place an order. The annual holding cost rate is 20%. With the order quantity of 500, Keith obtains the shoes at the lowest possible unit cost of $28 per pair. Other quantity discounts offered by the manufacturer are as follows:
a. What is the minimum cost order quantity for the shoes?
b. What are the annual savings of your inventory policy over the policy currently being used by Keith?
Discount Category Order Quantity Price Per Pair 1 0 to 99 $36 2 100 to 199 $32 3 200 to 299 $30 4 300 or More $28Explanation / Answer
We now find Q* for each category using the formula
Q*= (2DO/k)
Then for each category we obtain:
C=36;
Q* = (2DO/k)
Q* = [(2*500*30)/(0.2*36)]
Q* = 65
C=32
Q* = (2DO/k)
Q* = [(2*500*30)/(0.2*32)]
Q* = 69
C=30
Q* = (2DO/k)
Q* = [(2*500*30)/(0.2*30)]
Q* = 71
C=28
Q* = (2DO/k)
Q* = [(2*500*30)/(0.2*28)]
Q* = 73
Now check if Q* order is in the acceptable range for each category:
Order 65. range 0-99 acceptable.
Order 69. range 100-199 not acceptable.
Reset order to 100(Closest range limit to 69).
Order 71. range 200-299 not acceptable.
Reset order to 200(Closest range limit to 71).
Order 73. range 300 or more not acceptable.
Reset order to 300(Closest range limit to 73).
Total annual cost for discount category 1
= (1/2)KQ*+(DO/Q*)+DP
= (1/2)*(0.2*36*65)+[(500*30)/65]+(500*36)
= 18464.77
Total annual cost for discount category 2
= (1/2)KQ+(DO/Q)+DP
= (1/2)*(0.2*32*100)+[(500*30)/100]+(500*3…
= 16470
Total annual cost for discount category 3
= (1/2)KQ+(DO/Q)+DP
= (1/2)*(0.2*30*200)+[(500*30)/200]+(500*3…
= 15675
Total annual cost for discount category 4
= (1/2)KQ+(DO/Q)+DP
= (1/2)*(0.2*28*300)+[(500*30)/300]+(500*2…
= 14890
The minimum total annual cost is $14890 for the discount category 4 with a minimum cost order quantity of 300 for the shoes.
Annual savings of my inventory policy
= Q(300)-Q(500)
={(1/2)*(0.2*28*300)+[(500*30)/300]+(5…
= 14890-15430
= -$540
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