Question

One of the top-selling items at a gift shop at Hilo, HI are autographed pictures of Jack Star. Sales are 18 pictures per week, and the supplier charges $60 per picture. Currently the gift shop orders a 6-week supply at one time from the supplier. The total cost of placing each order is $45. Annual holding costs are $15 per picture. Assume that the shop operates 52 weeks/year.
A) What is the shop's current average inventory level?
B) What is the shop's current annual inventory holding cost?
C) What is the shop's current annual ordering cost (total cost of placing orders over the entire year)?
D) If the shop wishes to minimize total annual cost, what size orders should be placed?
E) At the optimal ordering quantity, what is the ordering and inventory holding cost per picture sold?
F) At the optimal ordering quantity, what is the shop's inventory turns per year?

Answer 1

Answer:

a. 54

b. 810 dollars

c. 390 dollars

d. 75 pictures

e. 561.6 dollars and 562.5 dollars

f. 38 pictures

Explanation:

demand per week = 18 pictures

annually this demand = 18 *52 = 936

charge per unit = 60 dollars

order for 6 weeks = 6*18 = 108 quantities

cost of ordering = 45 dollars

cost of holding annually = 15 dollars

a. current average inventory

= (18*6)/2

= 54 pictures

b. current annual holding cost

(108/2)*15

= 810 dollars

c. current annual holding cost

= 936/108 * 45

= 390 dollars

d. size orders to be placed

= $\sqrt{\frac{2*936*45}{15} }$

= $\sqrt{5616}$

= 74.9

≈ 75 pictures have to be ordered

e. ordering holding cost per picture

936/75 * 45

= 561.6 dollars

and inventory holding cost per picture

= 75/2 * 15

=562.5 dollars

f. shop inventory per year at optimal ordering quantity

= 75/2

= 37.5

≈ 38 pictures