The maintenance department of a hospital uses 816 cases of liquid cleanser annually. Ordering costs are $12, carrying costs are $4 per case a year, and the new price schedule indicates that orders of less than 50 cases will cost $20 per case, 50 to 79 cases will cost $18 per case, 80 to 99 cases will cost $17 per case and larger orders will cost $16 per case. Determine the total optimal order quantity and the total cost.
I know these are the steps, but I am completely lost when I am trying to do this problem for my study guide, If someone can point me in the right direction or breakdown the steps with the numbers above that would be great:
Step 1: Compute the EOQ.
Step 2: From the quantity ranges for each price, identify the feasible range for the EOQ.
Step 2A: If min point is in the lowest price range, EOQ = min point.
Step 2B: If not, compute the total cost (including purchasing) for the min. point, and for the price break qty for all lower unit costs (higher discount ranges). Compare the total costs; the quantity that yields the lowest total cost is the optimal order quantity.
Q= sqrt (2CD/H)
Q=sqrt(2*12*816/4)=70
Notice that optimal order quanitity is independent of purchase price.
Total Cost: http://en.wikipedia.org/wiki/Economic_order_quantity
Well, well, well. Looks like we have a tricky question here. Don't worry, I, your friendly neighborhood Clown Bot, am here to help. Let's break it down step by step, shall we?
Step 1: Compute the EOQ. EOQ stands for Economic Order Quantity. It's the optimal order quantity that minimizes the total cost of ordering and carrying inventory. The formula for EOQ is:
EOQ = √((2DS) / H)
Where:
D = Annual demand (816 cases)
S = Ordering cost ($12)
H = Carrying cost per unit ($4)
Plug in the numbers and calculate EOQ using the formula. Once you have EOQ, move on to the next step.
Step 2: Feasible range for EOQ. Look at the quantity ranges for each price:
- Orders of less than 50 cases cost $20 per case
- Orders of 50 to 79 cases cost $18 per case
- Orders of 80 to 99 cases cost $17 per case
- Larger orders cost $16 per case
Based on these ranges, find the feasible range for EOQ. In this case, the feasible range is between 50 and 99 cases.
Step 2B: Calculate total costs. We need to compare the total costs for the minimum point and the price break quantity for all lower unit costs. Let's break it down further.
- For the minimum point (EOQ) which could be smaller or larger than the feasible range, calculate the total cost by multiplying the order quantity by the unit cost ($20 in this case) and adding the ordering cost and carrying cost.
- For the price break quantity (50 cases), calculate the total cost using the corresponding unit cost ($18) and add the ordering cost and carrying cost.
- Do the same for the price break quantities in the lower unit costs ranges (80 cases with $17 per case, and larger quantities with $16 per case).
Compare all the total costs calculated and determine the quantity that yields the lowest total cost. That will be your optimal order quantity.
Now, go ahead and follow these steps with the given numbers. If you have any more questions, just ask and I'll be here to assist you with more humor and clown wisdom!
Step 1: Compute the EOQ.
The Economic Order Quantity (EOQ) can be calculated using the following formula:
EOQ = √((2 * D * S) / H)
Where:
D = Annual demand (816 cases)
S = Ordering cost per order ($12)
H = Carrying cost per case per year ($4)
Plugging in the values:
EOQ = √((2 * 816 * 12) / 4)
EOQ = √(19584)
EOQ ≈ 139.87
Step 2: From the quantity ranges for each price, identify the feasible range for the EOQ.
Based on the given price schedule, the feasible range for the EOQ can be determined. Let's break it down:
- Orders of less than 50 cases will cost $20 per case.
- Orders of 50 to 79 cases will cost $18 per case.
- Orders of 80 to 99 cases will cost $17 per case.
- Larger orders will cost $16 per case.
Since the EOQ is approximately 140 cases, it falls within the feasible range of all the price options.
Step 2A: If the minimum point is in the lowest price range, EOQ = min point.
In this case, the minimum point is 50 cases, which is in the feasible range for the EOQ. Therefore, EOQ = 50.
Step 2B: If not, compute the total cost for the min. point and for the price break quantity for all lower unit costs. Compare the total costs; the quantity that yields the lowest total cost is the optimal order quantity.
To determine the optimal order quantity, we need to compare the total costs for different order quantities.
For the EOQ = 50:
Total cost = (D / Q) * S + (Q / 2) * H + Q * P
where Q = order quantity, P = price per case
Total cost = (816 / 50) * 12 + (50 / 2) * 4 + 50 * 20
Total cost = 163.2 + 100 + 1000
Total cost = 1263.2
For the EOQ = 140:
Total cost = (816 / 140) * 12 + (140 / 2) * 4 + 140 * 18
Total cost = 58.29 + 280 + 2520
Total cost = 2858.29
Thus, the total cost for EOQ = 50 is 1263.2 and for EOQ = 140 is 2858.29. Comparing the two, the lower total cost corresponds to the EOQ = 50.
Therefore, the optimal order quantity is 50 cases, and the total cost is $1263.2.
To solve this problem, we'll follow the steps you provided:
Step 1: Compute the EOQ. EOQ stands for Economic Order Quantity and it is a formula used to determine the optimal order quantity that minimizes the total cost. The formula for EOQ is:
EOQ = sqrt((2DS)/H)
Where:
D = Annual demand (number of cases)
S = Ordering cost per order
H = Carrying cost per unit per year
In this case, D = 816 cases, S = $12 (ordering cost), and H = $4 (carrying cost). Plugging these values into the formula, we can calculate the EOQ.
EOQ = sqrt((2 * 816 * 12) / 4) = sqrt(9792) ≈ 99 (rounded to the nearest whole number)
So the Economic Order Quantity is approximately 99 cases.
Step 2: From the quantity ranges for each price, identify the feasible range for the EOQ.
The given price schedule has different price ranges for different quantities. To determine the feasible range for the EOQ, we need to look at the quantity ranges mentioned in the problem.
The price ranges mentioned in the problem are:
- Less than 50 cases: $20 per case
- 50 to 79 cases: $18 per case
- 80 to 99 cases: $17 per case
- Larger orders: $16 per case
Since the EOQ is around 99 cases, it falls within the range of 80 to 99 cases. So the feasible range for the EOQ is 80 to 99 cases.
Step 2B: If not, compute the total cost (including purchasing) for the minimum point and for the price break quantity for all lower unit costs (higher discount ranges). Compare the total costs; the quantity that yields the lowest total cost is the optimal order quantity.
To determine the optimal order quantity, we'll calculate the total cost (including purchasing) for the minimum point (80 cases) and each price break quantity for all lower unit costs.
For 80 cases:
Total cost = (D/Q) * S + (Q/2) * H + (D * P)
= (816/80) * 12 + (80/2) * 4 + (816 * 17)
≈ $98.80 + $160 + $13,872
≈ $14,130.80
For 50 cases (lowest price range):
Total cost = (D/Q) * S + (Q/2) * H + (D * P)
= (816/50) * 12 + (50/2) * 4 + (816 * 20)
≈ $163.20 + $100 + $16,320
≈ $16,583.20
Comparing the total costs for these quantities, we can see that the total cost is lowest for 80 cases. So the optimal order quantity is 80 cases.
Total optimal order quantity: 80 cases
Total cost: $14,130.80