The soft goods department of a large department store sells 175 units per month of a certain large bath towel. the unit cost of a towel to the store is $2.50 and the cost of placing an order has been estimated to be $12.00. the store uses an inventory carrying charge of i = 27% per year. the lead time for the large bath towel, from the supply chain, takes 5 days. determine the following: a. what is the optimal order quantity? b. what are the number of orders? c. what is the cost of managing the inventory d. if the department store is open 350 days per year, how many days are between orders? e. if the lead time from the supplier takes 10 days, what is the re-order point?

a 272.24 units, b 7.71, c $92.56, d 15 - 23days e 21,000units

Explanation:

Demand = 175 × 12 = 2,100 unit per annum

Holding Cost = $2.50 × 27%

= $0.68

Ordering cost =$12.00

Using the formula EOQ = √ 2DS / H

Where D = 2,100, S= $12.00, H = 0.68

EOQ = √ 2 × 12.00 × 2,100/ 0.68

= √50,400/0.68

= √ 74,117.64

= 272.24 units

b to calculate number of orders, we use D/Q

D = 2,100, Q = 272.24

= 2,100/272.24

= 7.71

c To calculate the cost of managing the orders, we use the formula THC = Q/2 × HC

= 272.24/2 × 0.68

= $92.56

d to calculate the lead time , we divide the number of days open in a year by addition of lead time

5 + 10 = 15

350÷ 15 = 23.3

Therefore the lead time is 15 - 23 days

e to calculate the Re order point we use the formula Demand × lead time

= 2,100 × 10

= 21,000 units

answer; /// the above statement is (true);