Bamazon Inc’s demand for a product is 15 units per month. Its supplier charges an ordering cost of $5 per order and $10 per unit with a 10% discount for orders of 15 units or higher. Bamazon Inc. incurs a 25% annual holding cost. What is its annual total cost (which includes the purchasing cost, ordering cost, and holding cost) the firm incurs, assuming they operate optimally?

Annual demand D = 15*12 = 180 units

Ordering cost S = $5

Holding cost H = 0.25*Cost per unit

Range Cost C Holding cost H
0-14 $10 =0.25*10 = 2.5
15 or above $9 =0.25*9 = 2.25
We know Optimal order quantity Q
https://latex.codecogs.com/gif.latex?Q%20%3D%20%5Csqrt%7B%5Cfrac%7B2DS%7D%7BH%7D%7D
We calculate Q at H = 2.5,2.25

H = 2.5

https://latex.codecogs.com/gif.latex?Q%20%3D%20%5Csqrt%7B%5Cfrac%7B2*180*5%7D%7B2.5%7D%7D

https://latex.codecogs.com/gif.latex?Q%20%3D%20%5Csqrt%7B%5Cfrac%7B2*180*5%7D%7B2.5%7D%7D
Q = 26.83 or 27

It is not feasible as it is not with in the range of 1-14

H= 2.25

https://latex.codecogs.com/gif.latex?Q%20%3D%20%5Csqrt%7B%5Cfrac%7B2*180*5%7D%7B2.25%7D%7D

Q = 28.28 or 28

It is feasible as it is in the range of above 15 units

Q = 28

Annual total cost = Purchasing cost + Annual ordering cost + Annual holding cost = CD + (D/Q)S + (Q/2)H

Annual total cost = 180*9 + (180/28)*5 + (28/2)*2.25 = 1620 + 32.14+31.5 = 1683.64

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