Answer :
To minimize the total annual holding and ordering cost, Greenmore Lawn Products should determine the economic order quantity (EOQ) for ammonium nitrate.
The EOQ formula is:
EOQ = √((2 × demand × ordering cost) / carrying cost)
Where:
- Demand is the annual requirement of ammonium nitrate (625,000 tons per quarter, so 2,500,000 tons per year)
- Ordering cost is $1,595 per order
- Carrying cost is 35% of the purchasing cost ($122.50 per ton)
Substituting the values into the formula, we get:
EOQ = √((2 × 2,500,000 × 1,595) / (0.35 × 122.50))
Simplifying the equation:
EOQ ≈ 13,638 tons
Therefore, Greenmore should buy approximately 13,638 tons of ammonium nitrate in each order to minimize the total annual holding and ordering cost.
Now, let's calculate the approximate total annual holding and ordering cost incurred if ammonium nitrate is ordered at the EOQ. The total holding cost is the carrying cost per ton multiplied by the EOQ divided by 2, and the total ordering cost is the ordering cost per order multiplied by the number of orders per year (which can be calculated by dividing the annual demand by the EOQ).
Total holding cost = (carrying cost × EOQ) / 2
= (0.35 × $122.50 × 13,638) / 2
≈ $292,373
Number of orders per year = annual demand / EOQ
= 2,500,000 / 13,638
≈ 183 orders
Total ordering cost = ordering cost per order × number of orders per year
= $1,595 × 183
≈ $292,185
Total annual holding and ordering cost ≈ total holding cost + total ordering cost
≈ $292,373 + $292,185
≈ $584,558
Therefore, the approximate total annual holding and ordering cost incurred if ammonium nitrate is ordered at the EOQ is approximately $584,558.
Moving on to the next question, let's calculate the approximate time between consecutive orders (in days) for Greenmore. We know that there are 365 days in a year, and we can use the formula:
Time between consecutive orders (in days) = 365 / (number of orders per year)
Substituting the value we found earlier:
Time between consecutive orders ≈ 365 / 183
≈ 2 days
So, the approximate time between consecutive orders for Greenmore is approximately 2 days.
Finally, let's calculate the approximate number of orders per year that Greenmore must place for ammonium nitrate if it orders the EOQ. We can use the same formula as before:
Number of orders per year = annual demand / EOQ
= 2,500,000 / 13,638
≈ 183 orders
Therefore, Greenmore must place approximately 183 orders per year if it orders the EOQ.
Moving on to the next question regarding lowa Book and Supply (IB&S) and the Harry Potter (HP) novel, to maximize IB&S's expected profit, we need to determine the order quantity that will result in the highest profit. In this case, we need to consider the retail price, wholesale price, salvage price, and demand for the HP novel.
The expected profit formula is:
Expected profit = (demand × (retail price - wholesale price)) - (demand - order quantity) × salvage price
Where:
- Demand is normally distributed with a mean of 200 copies and a standard deviation of 80 copies.
- Retail price is $20 per copy.
- Wholesale price is $12 per copy.
- Salvage price is $8 per copy.
To find the order quantity that maximizes expected profit, we need to find the value of z from Table 13-4. Since we are looking for the highest profit, we need to find the z value that corresponds to the highest probability, which is the standard deviation value of 80.
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