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Answer:
or ordering quantity 1-9,
EOQ = sqrt((2*annual demand*ordering cost)/holding cost per unit per year) = sqrt((2*10000*75)/(20%*2.95)) = 1594.48201
Optimal ordering quantity will not be in this range as calculated EOQ is beyond the range
For ordering quantity 10-999,
EOQ = sqrt((2*annual demand*ordering cost)/holding cost per unit per year) = sqrt((2*10000*75)/(20%*2.5)) = 1732.050808
Optimal ordering quantity will not be in this range as calculated EOQ is beyond the range
For ordering quantity 1000-4999,
EOQ = sqrt((2*annual demand*ordering cost)/holding cost per unit per year) = sqrt((2*10000*75)/(20%*2.3)) = 1805.787796
Total annual cost = ordering cost + holding cost + purchase cost = (10000/1805.787796)*75+(1805.787796/2)*(20%*2.3)+10000*2.3 = 23830.66239
For ordering quantity 5000 or more,
EOQ = sqrt((2*annual demand*ordering cost)/holding cost per unit per year) = sqrt((2*10000*75)/(20%*1.85)) = 2013.468166
EOQ is adjusted upwards to 5000 to avail the discount
Total annual cost = ordering cost + holding cost + purchase cost = (10000/5000)*75+(5000/2)*(20%*1.85)+10000*1.85 = 19575
So, optimal ordering quantity = 5000
Firm should pay $1.85 per unit
Annual cost at the optimal behavior = 19575
Explanation:
Following are the solution to the given question:
Quantity 1-9,
[tex]\to EOQ =\sqrt{ \frac{(2 \times \text{annual demand} \times \text{ordering cost})}{\text{(holding cost per unit per year)}}}[/tex]
[tex]= \sqrt{\frac{(2\times 10000 \times 75)}{(20\%\times 2.95)}}\\\\ = 1594.48201[/tex]
Since the EOQ is not inside Quantity 1-9, we will continue to the next range.
Quantity 10-999,
[tex]\to EOQ =\sqrt{ \frac{(2 \times \text{annual demand} \times \text{ordering cost})}{\text{(holding cost per unit per year)}}}[/tex]
[tex]= \sqrt{\frac{(2\times 10000 \times 75)}{(20\% \times 2.5)}}\\\\ = 1732.050808[/tex]
Since the EOQ does not fall inside the Quantity 10-999 range, we will proceed to the next range.
Quantity 1000-4999,
[tex]\to EOQ =\sqrt{ \frac{(2 \times \text{annual demand} \times \text{ordering cost})}{\text{(holding cost per unit per year)}}}[/tex]
[tex]= \sqrt{\frac{(2\times 10000 \times 75)}{(20\% \times 2.3)}}\\\\= 1805.787796[/tex]
[tex]\to \text{Annual total cost = annual ordering cost}+\text{annual inventory cost+ purchase cost}[/tex]
[tex]= (\frac{10000}{1805.787796})\times 75+(\frac{1805.787796}{2})\times (20\% \times 2.3)+10000 \times 2.3\\\\= (\frac{10000}{1805.787796})\times 75+(\frac{1805.787796}{2})\times (\frac{20}{100} \times 2.3)+10000 \times 2.3\\\\= (\frac{10000}{1805.787796})\times 75+1805.787796\times 0.23+23000 \\\\ = 23830.66239[/tex]
Quantity 5000+
[tex]\to EOQ =\sqrt{ \frac{(2 \times \text{annual demand} \times \text{ordering cost})}{\text{(holding cost per unit per year)}}}[/tex]
[tex]= \sqrt{\frac{(2\times 10000 \times 75)}{(20\% \times 1.85)}}\\\\= 2013.468166[/tex]
EOQ is adjusted upwards to 5000 to avail of the discount.
[tex]\to \text{Annual total cost = annual ordering cost}+\text{annual inventory cost+ purchase cost}[/tex] [tex]= (\frac{10000}{5000}) \times 75+(\frac{5000}{2})\times (20\% \times 1.85)+10000 \times 1.85 \\\\= (\frac{10}{5}) \times 75+(2500)\times (20\% \times 1.85)+10000 \times 1.85 \\\\= 2 \times 75+(2500)\times (0.20 \times 1.85)+10000 \times 1.85 \\\\= 150+(2500)\times (0.37)+ 18500 \\\\= 150+925+ 18500 \\\\= 19575[/tex]
- 5000 is the optimal ordering quantity.
- That company should pay $1.85 for each unit.
- Total annual cost based on best behavior = 19575.
- The overall price of holding is based on development adequately.[tex]= (\frac{5000}{2}) \times (20\% \times 1.85)\\\\= (2500) \times (0.20 \times 1.85)\\\\ = 925[/tex]
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