The S&H Mercantile in Luther is the only game in town for a number of items, and tries valiantly to use only the storage space needed to display items since there is no stock room in the back of the store. One popular item, a 16-ounce can of dehydrated water, takes up 20 square inches of shelf space. The shelf space available for this item measures five feet by four feet. The store manager would like to order a quantity that can fill the shelf space without stacking and without needing to store cans elsewhere in the store. The amount ordered should all be on display once the S&H runs out and ideally would arrive just as the last can is purchased. A. Suppose the annual demand is 8,000 units and the cost per can is $3 with a holding cost of 10%. What is the required order cost per lot?
B. Drought conditions spike demand during the summer to an annualized rate of 27,000 cans per year and the price rises to $12 per can with a holding cost of 20%. What is the required order cost per lot?

A. The required order cost per lot is $0.388

B. The required order cost per lot is $0.9216

Explanation:

A. According  to the given data Given area of shelf space = 5 Ft * 4 Ft = 20 Sq. Ft

Let us covert it to Sq. inch

1 Ft = 12 Inches

Therefore , Area of shelf space = 20 *12 * 12 = 2,880 Sq. in

1 can of water takes 20 Sq inch of shelf space

Therefore no. of cans that the shelf space can hold = 2880 / 20 = 144 Cans

Now SH wants to store exact amount of shelf space without needing to store cans somewhere elseand hence this 144 cans becomes EOQ (Economic order Qty.)

Now we know EOQ = √(2KD) / h Eq. 1

EOQ = 144

K = Fixed ordering cost = ?

D = Annual demand = 8000

h = Holding cost = ?

C = Cost per can = $ 3

i = 10 % (Carrying cost as percentage of Unit cost)

h = i * C

h = 10 % * $ 3

h = $ 0.3

Substituting above in Eq. 1 and solve for K

EOQ = √ (2KD) / h

144 = √(2 * K * 8000) / 0.3

Squaring both sides we get

20,736 = (16,000 * K ) / 0.3

20,736 * 0.3 = 16,000 * K

K = 6220.8 /16000

K = $ 0.388 = Ordering cost per order

The required order cost per lot is $0.388

B.  Here EOQ remains same = 144  But other parameters change

K = Fixed ordering cost = ?

D = Annual demand = 27,000

h = Holding cost = ?

C = Cost per can = $ 12

i = 20 % (Carrying cost as percentage of Unit cost)  

h = i * C

h = 20 % * $ 12

h = $ 2.4

Substituting above in Eq. 1 and solve for K

EOQ =√(2KD) / h

144 =  √(2 * K * 27,000) / 2.4

Squaring both sides we get

20,736 = ( 54,000 * K ) / 2.4

20,736 * 2.4 = 54,000 * K

K = 49,766.4 /54,000

K = $ 0.9216 = Ordering cost per order

The required order cost per lot is $0.9216

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