options(scipen = 999, digits=2)

1. Draw a process flow diagram for DEF Electronics.

2. Calculate the current weekly production capacity for the Module Fabrication Department.

num_machines <- 7  # Of the 8, one is usually under maintenance
num_operator <- 6  # excluding the 2 internally available
num_labour <- min(num_machines, num_operator)  # only as fast as the bottleneck

modules_per_hour <- 30
hours_per_week <- 5 * 8  # 5 days, with 8-hour shift (exclude break)
fab_prod_capacity <- modules_per_hour * hours_per_week * num_labour
fab_units_per_hour <-  modules_per_hour * num_labour

Module Fabrication Department Weekly Production Capacity: 7200 units

3. Calculate the weekly production capacity for the Final Assembly Department.

assembly_units_per_hour <- 140
hours_per_week <- 5 * 8  # 5 days, with 8-hour shift (exclude break)
assembly_prod_capacity <- assembly_units_per_hour * hours_per_week

Final Assembly Department Weekly Production Capacity: 5600 units

4. Which department is the current bottleneck, and why?

Currently the Final Assembly Department is the bottleneck as the Module Fabrication Department produces 180 units per hours, but the Final Assembly has a lower capacity of producing 140 units per hour.

5. Compute the labor cost per module in the Module Fabrication Department.

modules_per_hour <- 30
labour_cost_per_hour <- 22  # Assuming no overtime.
fab_labour_cost_per_module <- labour_cost_per_hour / modules_per_hour

Module Fabrication Department labour cost per module: $0.73

6. Compute the labor cost per module in the Final Assembly Department.

modules_per_hour <- 140
labour_cost_per_hour <- 19 * 12
assembly_labour_cost_per_module <- labour_cost_per_hour / modules_per_hour

Final Assembly Department labour cost per module: $1.63

7. Calculate the total variable cost per module, including fabrication, assembly, and purchased components.

material_cost_per_mod <- 0.4
electricity_cost_per_mod <- 0.08
var_cost_fab_per_mod <- (
    material_cost_per_mod + electricity_cost_per_mod + fab_labour_cost_per_module
)

component_price_per_mod <- 0.6
var_cost_assembly_per_mod <- component_price_per_mod + assembly_labour_cost_per_module

total_variable_cost_per_mod <- var_cost_fab_per_mod + var_cost_assembly_per_mod

Total variable cost per module: $3.44

8. If each module sells for $4.00, calculate the contribution margin per unit.

contribution_margin_per_unit <- 4 - total_variable_cost_per_mod

Contribution margin per unit: $0.56

9. If two more operators are added to the fabrication department, what is the new weekly capacity of the fabrication department?

num_machines <- 7  # Of the 8, one is usually under maintenance
num_operator <- 8  # including the 2 internally available
num_labour <- min(num_machines, num_operator)  # only as fast as the bottleneck

modules_per_hour <- 30
hours_per_week <- 5 * 8  # 5 days, with 8-hour shift (exclude break)
fab_prod_capacity <- modules_per_hour * hours_per_week * num_labour

Weekly fabrication department capacity with 2 more operators: 8400

10. If the assembly department adds a second shift (doubling hours), what is the new overall process capacity?

modules_per_hour <- 140
hours_per_week <- 5 * 8 * 2 # 5 days, with 2 8-hour shift (exclude break)
assembly_prod_capacity <- modules_per_hour * hours_per_week

New fabrication department capacity: 8400
New assembly department weekly capacity: 11200

New Overall Process Capacity: 8400 units per week
Bottleneck is now fabrication department

11. How many overtime hours per operator would be required in fabrication to match the assembly capacity fully?

modules_per_hour <- 30
num_overtime_units <- assembly_prod_capacity - fab_prod_capacity
extra_manhour <- num_overtime_units / modules_per_hour

num_operator <- 8
overtime_per_operator <- extra_manhour / num_operator

Overtime hours per operator per week: 11.67 hours

12. What is the labor cost per module for the overtime units?

overtime_wage <- 22 * 150 / 100
cost_per_overtime <- (extra_manhour * overtime_wage) / num_overtime_units

Labour cost per overtime units: $1.10