A manufacturer of hospital supplies has a uniform annual demand for 80,000 boxes of
bandages. It costs $10 to store one box of bandages for one year and $160 to set up
the plant for prduction. Haw many times a year should the company produce boxes
of bandages in order to minimize the total storage and setup costs?
To minimize the total storage and setup costs, we need to determine the optimal production quantity. Let's use the Economic Order Quantity (EOQ) formula:
EOQ = √((2DS) / H)
Where:
D = Annual demand = 80,000 boxes
S = Setup cost = $160
H = Annual holding cost per box = $10
Substituting the given values into the formula:
EOQ = √((2 * 80,000 * $160) / $10)
EOQ = √((32,000,000) / $10)
EOQ = √(3,200,000)
EOQ ≈ 178.9 (rounded to the nearest whole number)
The optimal production quantity, in this case, is approximately 179 boxes of bandages.
To determine how many times a year the company should produce boxes of bandages, we need to calculate the production frequency:
Production frequency = (Annual demand) / (EOQ)
Production frequency = 80,000 / 179
Production frequency ≈ 446.9
Rounded to the nearest whole number, the company should produce boxes of bandages approximately 447 times a year to minimize the total storage and setup costs.
To minimize the total storage and setup costs, we need to determine how many times a year the company should produce boxes of bandages.
Let's break down the problem and find the optimal solution step by step:
1. Calculate the Economic Order Quantity (EOQ):
The EOQ formula is given by:
EOQ = sqrt((2DS) / H)
Where:
D = Annual demand of boxes of bandages = 80,000
S = Setup cost per production run = $160
H = Holding cost per box per year = $10
Substituting the given values, we have:
EOQ = sqrt((2 * 80,000 * $160) / $10)
2. Calculate the Optimal Order Quantity (Q):
The optimal order quantity is given by rounding up the EOQ to the nearest whole number or the most practical production run size for the manufacturer.
Q = ceil(EOQ)
3. Calculate the Production Frequency:
Production frequency is the number of times the company should produce bandages in a year to meet the optimal order quantity.
Production frequency = D / Q
Substituting the given values, we have:
Production frequency = 80,000 / Q
4. Determine the optimal number of production runs per year:
To minimize costs, the company should aim to produce whole numbers of bandages boxes. Therefore, we need to find the optimal whole number that minimizes the total storage and setup costs.
The total storage and setup costs can be calculated as:
Total cost = (D / Q) * S + (Q / 2) * H
By plugging in the values for Production frequency (D / Q) and the given values for S and H, we can calculate the total cost.
5. Repeat steps 2-4 with different values for Q until you find the optimal number of production runs per year that minimizes the total cost.
Using this approach, you can find the exact number of times the company should produce boxes of bandages in order to minimize the total storage and setup costs.
Seems like we need to know something about the production of bandages. Is it continuous? Instant batches of some fixed number? Production over a period of days?
Is the consumption to be considered a continuous function?
I see no way to solve this with the information given.