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In: Statistics and Probability

Apply the EOQ model to the following quantity discount situation in which D = 400 units...

Apply the EOQ model to the following quantity discount situation in which D = 400 units per year, Co = $36, and the annual holding cost rate is 25%.

Discount Category	Order Size	Discount (%)	Unit Cost
1	0 to 99	0	$10.00
2	100 or more	4	$9.60

What order quantity do you recommend? If required, round your answer to the nearest whole number.

***answer is not 4

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Expert Solution

SOLUTION:

From given data,

Apply the EOQ model to the following quantity discount situation in which D = 400 units per year, Co = $36, and the annual holding cost rate is 25%.

D = 400 units per year

Co = $36

holding cost rate = 25% = 25/100 = 0.25

Discount Category	Order Size	Discount(%)	Unit Cost
1	0 to 99	0	$ 10.00
2	100 or more	4	$ 9.60

We have to find order quantity.

Economic order quantity (Q_odt) = sqrt (20 * k / h)

Annual carrying cost per unit (h) = P * (h/p)

= $10 * 0.25

= $ 2.5

(Q_odt) = sqrt (20 *400*36 / 2.5)

(Q_odt) = sqrt (288000 / 2.5)

(Q_odt) = sqrt (115200)

(Q_odt) = 339.41

The number of order per year is = D / Q_odt

= 400 / 339.41

= 1.17

That is 2 orders.

The order of quantity for first one is 2 orders.

Economic order quantity (Q_opt) = sqrt (20 * k / h)

D = 400 units per year

Co = $36

p = $ 9.60

holding cost rate = 25% = 25/100 = 0.25

Annual carrying cost per unit (h) = P * (h/p)

= $ 9.60* 0.25

= $ 2.4

(Q_opt) = sqrt (20 *400*36 / 2.4)

(Q_opt) = sqrt (288000 / 2.4)

(Q_opt) = sqrt (120000)

(Q_opt) = 346.41

The number of order per year is = D / Q_opt

= 400 / 339.41

= 1.154

That is 2 orders.

The order of quantity for second one is 2 orders.

Therefore economic order quantity is recommend .

orchestra answered 1 year ago

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