Math Problem Statement

Per machine cost - 30 dollar Running machine - 3000 No of line - 85 Line manpower - 30 Working Hour - 10 Avarage SMV - 4.2 Working day - 26

What is the per line cost? What is the factory's cost per minute? What is the factory's cost of making ?

Solution

To analyze the given information, we will calculate the following:

1. Per Line Cost

To find the per line cost, we will account for the per-machine cost, the number of running machines, and the line manpower.

Per Line Cost=(Per Machine Cost×Number of Machines per Line)+(Line Manpower Cost per Day×Daily Wage per Manpower)\text{Per Line Cost} = (\text{Per Machine Cost} \times \text{Number of Machines per Line}) + (\text{Line Manpower Cost per Day} \times \text{Daily Wage per Manpower})

However, without a specific daily wage per manpower, this calculation will assume only the machine and manpower costs provided.

2. Factory's Cost per Minute

To determine the factory's cost per minute, we need the total daily cost and divide it by the total working minutes in the factory.

Total Daily Cost=(Per Machine Cost×Total Machines)+(Total Line Manpower Cost)\text{Total Daily Cost} = (\text{Per Machine Cost} \times \text{Total Machines}) + (\text{Total Line Manpower Cost}) Total Working Minutes=(Working Hours×60 minutes)×Total Lines\text{Total Working Minutes} = (\text{Working Hours} \times 60 \text{ minutes}) \times \text{Total Lines} Cost per Minute=Total Daily CostTotal Working Minutes\text{Cost per Minute} = \frac{\text{Total Daily Cost}}{\text{Total Working Minutes}}

3. Factory's Cost of Making

To calculate the factory's cost of making (cost per unit produced), we’ll use the following:

Factory Cost per Unit=Cost per Minute×Average SMV\text{Factory Cost per Unit} = \text{Cost per Minute} \times \text{Average SMV}

Let’s start the calculations based on these formulas.### Calculated Results:

  1. Per Line Cost: $1058.82
  2. Factory's Cost per Minute: $1.76
  3. Factory's Cost of Making (per unit based on average SMV): $7.41

Would you like a breakdown of these calculations or to provide additional details?


Additional Questions for Deeper Insight:

  1. What would be the impact on the cost per line if the number of machines or manpower per line increased?
  2. How does the per unit cost change if the average SMV varies?
  3. What is the overall monthly cost if we consider the number of working days?
  4. How would adjustments in working hours impact the factory’s cost per minute?
  5. What would be the effect of maintenance costs on the factory's total cost per minute?

Tip:

Analyze SMV values regularly, as they significantly impact production costs per unit.

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Math Problem Analysis

Mathematical Concepts

Cost Analysis
Rate Calculation
Factory Production Costs

Formulas

Per Line Cost = (Per Machine Cost × Machines per Line) + (Line Manpower Cost per Day)
Cost per Minute = Total Daily Cost / Total Working Minutes
Factory Cost per Unit = Cost per Minute × Average SMV

Theorems

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Suitable Grade Level

Grades 11-12