Consider a product with a daily demand of 400 units, a setup cost per production run of $100, a holding cost per unit of $24.00, and an annual production rate of 292,000 units. The firm operates and experiences demand 365 days per year. a. What is the Production Order Quantity?

b. What is the max inventory on hand?

c. What is the average inventory?

d. What are the total holding costs?

e. What does it cost to manage the inventory?

a 1,560 units

b 780 units

c 390 units

d $18,720

e $9,360

Explanation:

Given that;

Production = 292,000

Daily demand , d = 400

Annual demand , D = 400 × 365 = 146,000

Production rate , P = 292,000 ÷ 365 = 800

Set up cost , Cs = $100

Holding cost , Ch = $24

a. What is the production order quantity

= √2 * D * Cs / CH × (p / p - d)

= √ 2 * 146,000 * 100/24 × (800/800-400)

= √1216666.6667 × 2

= √2433333.3334

= 1559.91

=1,560 units approximated.

b. What is the maximum inventory on hand

= EPQ × [ 1 - (d÷p) ]

= 1,560 × [ 1 - (400 ÷ 800) ]

= 1,560 × 0.5

= 780 units

c. What is the average inventory

= Maximum inventory ÷ 2

= 780 ÷ 2

= 390 units

d. What are the total holding costs

= EOQ/2 * Holding cost

= 1,560/2 * 24

= 780 *24

= $18,720

e. What does it cost to manage the inventory

= Holding cost * (Maximum inventory ÷ 2)

= 24 * (780 ÷ 2)

= 24 * 390

= $9,360

answer; the cpi;