91Ó°ÊÓ

Step 1: Economic Order Quantity (EOQ)

This is determined by differentiating and locating the minima for the equation for the total yearly cost, which includes the variable purchase cost, ordering cost, and inventory holding cost. However, the EOQ is unaffected by the purchase cost because it remains constant for the same yearly demand regardless of order size.The overall cost, which includes both of these charges, is at its lowest at the EOQ value.

Given,

Monthly demand of T-shirt = 3000 × 3 = 9000 units

Cotton required per shirt = 0.5

Cost per pound of cotton (C) = $ 2. 2.50 + $ 0.20 = $ 2.70

Ordering cost (S) = $ 100 per order

Holding cost = 20 % of cost

Lead time (L) = 2 weeks

The monthly demand of the shirts is 9000 shirts and each shirt uses 0.5 pound of cotton. Thus, the annual demand of cotton becomes:

Annual demand = Monthly demand of shirts × cotton per shirt × 12 months

= 9,000 × 0.5 × 12

= 54,000 pounds of cotton

The holding cost of 20% of the cost price.

Holding cost = 20 % of cost

= 0.20 × $ 2.70

= $ 0.54

Calculation of economic order quantity

$$\begin{gathered} \mathrm{EOQ}=\sqrt{\frac{2×\mathrm{A}×\mathrm{S}}{\mathrm{H}}} \\ \mathrm{Where}, \\ \mathrm{A}=\mathrm{Annual}\mathrm{Demand} \\ \mathrm{S}=\mathrm{Ordering}\mathrm{cost}\mathrm{per}\mathrm{unit} \\ \mathrm{H}=\mathrm{Carrying}\mathrm{cost}\mathrm{per}\mathrm{unit} \\ \mathrm{EOQ}=\sqrt{\frac{2×\mathrm{A}×\mathrm{S}}{\mathrm{H}}} \\ =\sqrt{\frac{2×54,000×100}{0.54}} \\ =4,472.14\mathrm{or}4473\mathrm{pounds} \end{gathered}$$

So, the optimal order quantity of cotton is 4,473 pounds.

The frequency of orders for cotton is calculated below :

Given,

Annual demand = 54,000 units

EOQ = 4,473 units

$$\begin{gathered} \mathrm{Frequency}\mathrm{of}\mathrm{orders}=\frac{\mathrm{Annual}\mathrm{Demand}}{\mathrm{EOQ}} \\ =\frac{54,000}{4,473} \\ =12.07\mathrm{or}12\mathrm{times}\mathrm{per}\mathrm{year} \end{gathered}$$

So, the company should order cotton 12 times every year which is effectively once a month.

If the first purchase is required on April 1, the corporation should place the order two weeks earlier, on March 18. This is due to the two-week lead period, which includes the travel time from the LGT facility to the SYM facility. As order quantity increases, the number of orders to be placed in the year lowers, and so the ordering cost drops, but inventory holding costs continue to rise.

Given,

Annual demand = 54,000 units

EOQ = 4,473 units

Calculation of the optimal order for the next year:

$$\begin{gathered} \mathrm{Number}\mathrm{of}\mathrm{orders}=\frac{\mathrm{Annual}\mathrm{demand}}{{\mathrm{Q}}_{\mathrm{opt}}} \\ =\frac{54,000}{4,473} \\ =12\mathrm{orders} \end{gathered}$$

So, the manufacturer will place 12 orders next year.

Calculation of annual holding cost:

Given,

EOQ = 4,473 units

Cost of storage per unit (H) = $ 0.54

$$\begin{gathered} \mathrm{Annual}\mathrm{Holding}\mathrm{Cost}=\frac{\mathrm{Q}}{2}×\mathrm{H} \\ =\frac{4,473}{2}×\$0.54 \\ =\$1,207.71 \end{gathered}$$

So, the annual holding cost for cotton is $ 1,207.71

Given,

Annual demand = 54,000

EOQ = 4,473 units

$$\begin{gathered} \mathrm{Annual}\mathrm{ordering}\mathrm{cost}=\frac{\mathrm{D}}{\mathrm{Q}}\left(\mathrm{S}\right) \\ =\frac{54,000}{4,473}×\$100 \\ =\$1,207.24 \end{gathered}$$

So, the annual ordering cost for the cotton is $ 1,207.24

With a 5-percentage-point yearly interest rate. The yearly holding fee will be $ 0.135. This unexpected decrease in holding costs will result in a significant rise in order size. The cost of purchasing ecstasy increased the ideal order size will increase the average inventory.