# Super K Beverage Company distributes a soft drink that has a constant annual demand rate of 4,600...

## Question:

Super K Beverage Company distributes a soft drink that has a constant annual demand rate of 4,600 cases. A 12-pack case of the soft drink costs Super K $2.25. Ordering costs are $20 per order, and inventory-holding costs are charged at 25 percent of the cost per unit. There are 250 working days per year, and the lead time is 4 days.

Find the economic order quantity and total annual cost, and compute the reorder point.

## Economic Order Quantity (EOQ):

EOQ refers to the optimum quantity that an organization should procure for its inventory. EOQ is calculated using the rate of demand, production cost, and other variables.

## Answer and Explanation:

*Given information:*

- Annual demand (A) is 4,600 cases
- Ordering cost (O) is $20 per order
- Carrying cost (C) is 25% of $2.25 i.e. 0.5625

*Calculation of EOQ:*

{eq}\begin{align*} {\rm\text{EOQ}} &= \sqrt {\dfrac{{{\rm\text{2AO}}}}{{\rm\text{C}}}} \\ &= \sqrt {\dfrac{{2 \times 4600 \times 20}}{{0.5625}}} \\ &= 572{\rm\text{ units}} \end{align*} {/eq}

*Calculation of the total annual cost is as follows:*

{eq}\begin{align*} {\rm\text{Total annual cost}} &= {\rm\text{Carrying cost}} + {\rm\text{Ordering Cost}}\\ &{\rm{ = }}\dfrac{{\rm\text{Q}}}{2}\left( {\rm\text{H}} \right) + \dfrac{{\rm\text{D}}}{{\rm\text{Q}}}\left( {\rm\text{S}} \right)\\ &= \dfrac{{572}}{2}\left( {0.56} \right) + \dfrac{{4,600}}{{572}}\left( {20} \right)\\ &= \$ 321 \end{align*} {/eq}

*Calculation of reorder point is as follows:*

{eq}\begin{align*} {\rm\text{Reorder point}}\left( {\rm\text{R}} \right) &= {\rm\text{Average demand}} \times {\rm\text{Lead time}}\\ &{\rm{ = }}\dfrac{{4600}}{{250}} \times 4\\ &= 73.6{\rm\text{ or }}74{\rm\text{ cases}} \end{align*} {/eq}

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from Business 112: Operations Management

Chapter 13 / Lesson 7