Respuesta :
Solution :
The data for the Garden Variety Flower shop is :
Monthly demand, d = 500 clay pots
Annual demand, D = 500 x 12
= 6000 clays
Price, p = $ 3.00 each
Annual carrying cost, h = 25% of price
[tex]$=\frac{25}{100} \times 3$[/tex]
= $0.75
Ordering cost, S = $ 25 per order
a). The optimal order quantity, EOQ
[tex]$EOQ=\sqrt{\frac{2DS}{h}}$[/tex]
[tex]$=\sqrt{\frac{2\times 6000 \times 25}{0.75}}$[/tex]
[tex]$=\sqrt{\frac{300000}{0.75}}$[/tex]
= 632.45
≈ 633
So, the optimal order quantity is 633 clay pots.
Therefore, the annual cost for optimal order quantity 633 clay pots,
[tex]$\text{Total annual cost}_1=\left(\frac{D}{Q} \times S \right) + \left(\frac{D}{2} \times h \right)$[/tex] [tex]$\text{Total annual cost}_1=\left(\frac{6000}{633} \times 25 \right) + \left(\frac{633}{2} \times 0.75 \right)$[/tex]
= 236.96 + 237.37
= 474.33
Now calculating the total annual cost for the optimal order quantity 1500 flower pots, as shown below:
[tex]$\text{Total annual cost}_2=\left(\frac{D}{Q} \times S \right) + \left(\frac{D}{2} \times h \right)$[/tex]
[tex]$\text{Total annual cost}_2=\left(\frac{6000}{1500} \times 25 \right) + \left(\frac{1500}{2} \times 0.75 \right)$[/tex]
= 100 + 562.5
= 662.5
Calculating the additional annual cost of the shipping is incurring by staying with the order size, i.e. 1500 flower pots as given below:
Extra cost = [tex]$\text{total annual cost}_2 - \text{total annual cost}_1 $[/tex]
= 662.5 - 474.3
= 188.2
So, the [tex]\text{additional annual cost}[/tex] is the shop [tex]\text{incurring}[/tex] by staying with this order size is 188.2
b). Calculating the average inventory level of the [tex]\text{optimal order quantity}[/tex] 1500 flowers plots :
Average inventory = Q/2
[tex]$=\frac{1500}{2}$[/tex]
= 750
Calculating the average percentage of the storage space :
[tex]$\text{Percentage of storage space} = \frac{\text{Extra cost}}{\text{average inventory}}\times 100$[/tex]
[tex]$=\frac{188.2}{750} \times 100$[/tex]
= 0.250 x 100
= 25 %
So, the benefit would be using the [tex]\text{optimal order quantity}[/tex] yield, i.e. 1500 flower plots is 25%.
