Answer:
annual demand = 1,215 bags of flour
ordering costs = $10 per order
annual carrying costs = $75 per bag
a. Determine the economic order quantity.
EOQ = √[(2 x S x D) / H]
EOQ = √[(2 x $10 x 1,215) / $75] = 18 bags of flour
b. What is the average number of bags on hand?
average number of bags on hand = 18 / 2 = 9
c. How many orders per year will there be?
total number of orders per year = 1,215 / 18 = 67.5 orders
d. Compute the total cost of ordering and carrying flour.
total cost of ordering flour = 67.5 x $10 = $675
since we assume that the company keeps operating after the year ends, we can use fractions when calculating the number of orders per year
total cost of carrying flour = 9 x $75 = $675
total cost of ordering and carrying flour = $1,350
The results in the large bakery are as follows:
(a). Economic Order Quantity = 18 Bags of Flour.
(b). Average Number of Bags on Hand = 9 Bags.
(c). Total Number of Orders Per Year = 67.5 orders.
(d). Total cost of ordering and carrying flour = $675.
The Economic Order Quantity is employed to undervalue the costs of the order.
The total costs contain the Fixed Cost and Variable costs. These costs include the acquisition costs from the supplier, ordering costs, and moving costs.
(a). Computation of Economic Order Quantity:
According to the given information,
Annual Demand(D) = 1,215 bags of flour
Ordering Costs(O)= $10 per order
Annual Carrying Costs(C) = $75 per bag
Apply the given values in the formula of Economic Order Quantity,
[tex]\text{Economic Order Quantity} = \sqrt{\dfrac{2 \times O \times D }{C} }\\\\\text{Economic Order Quantity} =\sqrt{\dfrac{2\times \$10 \times \$1,215}{\$75} }\\\\\text{Economic Order Quantity} = 18 \text{bags}[/tex]
Therefore, the Economic Order Quantity is 18 bags.
(b). Computation of the average number of bags on hand:
[tex]\text{Average Number of Bags on Hand} =\dfrac{ \text{Economic Order Quantity}}{2}\\\text{Average Number of Bags on Hand} =\dfrac{18}{2}\\\\\text{Average Number of Bags on Hand} =9 \text{bags}[/tex]
(c). Computation of total numbers of orders per year:
[tex]\text{Total Number of Orders Per Year} = \dfrac{\text{Actual Demand}}{\text{Economic Order Quantity}}\\\\\text{Total Number of Orders Per Year} = \dfrac{1,215}{18}\\\\\text{Total Number of Orders Per Year} =67.5\text{Orders}[/tex]
(d). Computation of the total cost of ordering and carrying flour:
[tex]\text{Total Cost of Ordering Flour} = \text{Total Numbers of Orders Per Year} \times \text{\text{Ordering Cost}}\\\text{Total Cost of Ordering Flour} =9 \times \$75\\\text{Total Cost of Ordering Flour} = \$675[/tex]
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