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