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Given,

Annual Demand = 25,750

Order cost = $250.00

The annual Holding cost is 33% of the purchase price which is $10

Where,

D = Annual Demand

S = Cost per Order

H = Holding Cost

$\begin{array}{rcl}\mathrm{EOQ}& =& \sqrt{\frac{2脳\mathrm{D}脳\mathrm{S}}{\mathrm{H}}}\\ & =& \sqrt{\frac{2脳25,750脳250}{\left(0.33\right)\left(10\right)}}\\ & =& 1975\mathrm{units}\end{array}$

So, the optimal Order Quantity is 1975 units

As per the given information, the weekly demand is 532 units with a lead time of 2 weeks and a standard deviation of 30 units per week.

Using excel and applying NORMSINV (0.95) we get the value of z of 1.64.

Substitute - 515(1) + (1.64)(25) = 556 Units

Hence, at the level of 556 units, a new order must be placed.

Given,

Annual Demand (D) =25,750

Cost per Order (S) =$250.00

Holding Cost( H) = (0.33)(10)

The annual Holding cost is 33% of the purchase price which is $10

$\begin{array}{rcl}\mathrm{Holding}\mathrm{cost}& =& \frac{\mathrm{Q}}{2}\left(\mathrm{H}\right)\\ & =& \frac{1975}{2}\left(0.33\right)\left(10\right)\\ & =& \$3,258.75\end{array}$

$\begin{array}{rcl}\mathrm{Ordering}\mathrm{cost}& =& \frac{\mathrm{D}}{\mathrm{Q}}\left(\mathrm{S}\right)\\ & =& \frac{25,750}{1975}\left(250\right)\\ & =& \$3,259.49\\ & & \end{array}$

So, the Holding cost is $3258.75 and the Ordering cost is $3,259.49

$$\begin{gathered} \mathrm{Annual}\mathrm{Demand}\left(\mathrm{D}\right)=25,750 \\ \mathrm{Cost}\mathrm{per}\mathrm{order}\left(\mathrm{S}\right)=\$250.00 \\ \mathrm{Holding}\mathrm{cost}\left(\mathrm{H}\right)=\left(0.33\right)\left(10\right) \end{gathered}$$

The annual Holding cost is 33% of the purchase price, which is $10

$\begin{array}{rcl}\mathrm{Holding}\mathrm{cost}& =& \frac{\mathrm{Q}}{2}\left(\mathrm{H}\right)\\ & =& \frac{2000}{2}\left(0.33\right)\left(10\right)\\ & =& \$3,300\end{array}$

role="math" localid="1650529887541" $\begin{array}{rcl}\mathrm{Ordering}\mathrm{cost}& =& \frac{\mathrm{D}}{\mathrm{Q}}\left(\mathrm{S}\right)\\ & =& \frac{25,750}{2000}\left(250\right)\\ & =& \$3,218.75\end{array}$

So, the Holding cost is $33,00 and the Ordering cost is $3,218.75

Calculation of Total cost with discount

Total annual cost with discount = Annual Holding Cost + Annual Ordering cost - (Ordering cost after price break x No of orders)

Total annual cost with discount = $3,300 + $3,218.75 - [50 x (25,750 / 2000)]

Total annual cost with discount = $6518.75 - $643.75 = $5,875

Calculation of Total cost without discount as per part b -

Total annual cost without discount = Annual Holding Cost + Annual Ordering Cost

= $3258.75+ $3,259.49 = $6518.24

From the above calculations, it seems that the cost incurred with a discount is lower than without a discount. So advantage should be taken with a price break.

Saving in Ordering Cost = $6518.24 - $5,875= $643.24

Therefore, the amount of $643.24 will be saved annually.