A manufacturing firm makes a production run of 3,750 pieces. Each piece is 78.30 millimeters long. The cost of material per meter of length is $2.40. Allowing 10% for waste and scrap, what is the material cost for the 3,750 pieces? Round to nearest dollar.
The total length of all the pieces is 3750 * 78.30 = <<3750*78.30=293625>>293,625 millimeters.
After accounting for waste and scrap, the total length needed is 293,625 + (293,625 * 0.10) = <<293625+(293625*0.10)=322987>>322,987.5 millimeters.
Converting to meters, this is 322,987.5 / 1000 = 322.9875 meters.
The material cost for the 3,750 pieces is 322.9875 * $2.40 = $<<322.9875*2.40=775.17>>775.17.
Rounded to the nearest dollar, the material cost is $775.
To calculate the material cost for the 3,750 pieces, we need to consider the length of each piece, the cost per meter of length, and the percentage allowed for waste and scrap.
First, let's calculate the total length of the 3,750 pieces. Since each piece is 78.30 millimeters long, we can convert this to meters by dividing by 1000:
Length per piece = 78.30 mm / 1000 = 0.0783 meters
Then, we calculate the total length for 3,750 pieces:
Total length = Length per piece * Number of pieces = 0.0783 meters * 3,750 = 293.625 meters
Next, we account for the 10% waste and scrap. To calculate the adjusted length, we multiply the total length by 1.1:
Adjusted length = Total length * (1 + Waste percentage/100) = 293.625 * 1.1 = 322.9875 meters
Finally, we calculate the material cost by multiplying the adjusted length by the cost per meter:
Material cost = Adjusted length * Cost per meter = 322.9875 meters * $2.40/meter ≈ $775.17
Therefore, the material cost for the 3,750 pieces, rounded to the nearest dollar, is approximately $775.
To calculate the material cost for the 3,750 pieces, we need to follow these steps:
Step 1: Calculate the total length of the 3,750 pieces.
Total length = Number of pieces × Length per piece
Total length = 3,750 × 78.30 millimeters
Step 2: Convert the total length from millimeters to meters.
Total length in meters = Total length in millimeters / 1,000
Step 3: Account for 10% waste and scrap.
Actual length required = Total length in meters + (Total length in meters × 0.1)
Step 4: Calculate the material cost.
Material cost = Actual length required × Cost of material per meter
Now let's perform the calculations:
Step 1: Calculate the total length of the 3,750 pieces.
Total length = 3,750 × 78.30 = 293,625 millimeters
Step 2: Convert the total length from millimeters to meters.
Total length in meters = 293,625 / 1,000 = 293.625 meters
Step 3: Account for 10% waste and scrap.
Actual length required = 293.625 + (293.625 × 0.1) = 293.625 + 29.3625 = 323.9875 meters
Step 4: Calculate the material cost.
Material cost = 323.9875 × $2.40 = $777.57 (rounded to the nearest dollar)
Therefore, the material cost for the 3,750 pieces is approximately $778.