Exercise 1(50)

In this exercise, we are given a scenario where we are selling seasonal products during the Christmas season. We have five resources that we will utilize to make four products, and the demands and revenues for each product are provided. The processing time for each product at each resource is also given. Our factory will operate for 25 days in a month, and we will work for 10 hours each day.

To find the resource that is the bottleneck, we need to identify which resource has the longest processing time for any of the products. In this case, the longest processing time is 2.5 hours per unit for Resource 1 for Product 1. Therefore, Resource 1 is the bottleneck.

To determine the actual flow rates of each product, we should calculate the total number of units that can be processed through the bottleneck resource in a month. The formula for this is as follows:

Actual flow rate = Demand / (Processing time per unit at bottleneck resource * Number of working hours per day * Number of working days per month)

Let's apply this formula to our scenario. The processing time per unit at the bottleneck resource for each product is 2.5 hours per unit for Resource 1 for Product 1. Therefore, we have:

• Product 1: Actual flow rate = 80 units / (2.5 hours / unit * 10 hours / day * 25 days / month) = 32 units per day
• Product 2: Actual flow rate = 100 units / (2 hours / unit * 10 hours / day * 25 days / month) = 83.33 units per day
• Product 3: Actual flow rate = 120 units / (2 hours / unit * 10 hours / day * 25 days / month) = 106.67 units per day
• Product 4: Actual flow rate = 100 units / (0.5 hours / unit * 10 hours / day * 25 days / month) = 200 units per day

Note: Since the Processing time for Product 4 is in hours per 0.5 unit, I converted it to 1 unit (by multiplying 0.5) in the formula above.

We can now calculate the actual output for each product per week and per month. For example, consider Product 1:

• Weekly output: Actual flow rate * Number of working days per week = 32 units per day * 5 (working days per week) = 160 units per week
• Monthly output: Weekly output * Number of working weeks per month = 160 units per week * 4 (working weeks per month) = 640 units per month

Exercise 1(10)

Suppose we are the only worker in the factory, and we could earn at least $18/hour in a local shop. By taking this job, we are giving up this opportunity. This wage can be considered as the wage paid for direct labor. Since we are the only worker, we do not have to distinguish between specific flow units that come out.

Assuming that adding more workers (two friends) to the factory will not change the processing times, and their wage is also $18/hour, the approach to calculating the cost of direct labor will not change. However, since we have added two more workers, the direct labor cost will increase by $72/hour (2 workers x $18/hour).

Exercise 1(10)

We have invested $1000 to install the resources. Let's calculate the profit per month by subtracting the cost of direct labor, the cost of indirect labor, expenses, and the depreciation of the resources from the net revenue. Let's assume that the cost of indirect labor and expenses remain the same, regardless of the number of workers. The net revenue for each product is calculated as follows:

Net revenue = Demand x Revenue per unit

Let's apply this formula to our scenario:

• Product 1: Net revenue = 80 units / month x $50 / unit = $4000
• Product 2: Net revenue = 100 units / month x $65 / unit = $6500
• Product 3: Net revenue = 120 units / month x $30 / unit = $3600
• Product 4: Net revenue = 100 units / month x $50 / unit = $5000

Let's calculate the profit per month:

Profit = Net revenue - Cost of Direct Labor - Cost of Indirect Labor - Expenses - Depreciation

Let's assume that the total cost of indirect labor and expenses is $5000/month. Also, let's assume that the depreciation for the resources is $833.33/month. Substituting these values into the formula for profit:

Profit = (Net revenue - Cost of Direct Labor) - Cost of Indirect Labor - Expenses - Depreciation

Profit = Net Revenue - (Direct Labor Cost + Cost of Indirect Labor + Expenses + Depreciation)

Profit = (Product 1 Net Revenue + Product 2 Net Revenue + Product 3 Net Revenue + Product 4 Net Revenue) - (Total Direct Labor Cost + Cost of Indirect Labor + Expenses + Depreciation)

Let's calculate the profit per month:

Profit = (Product 1 Net Revenue + Product 2 Net Revenue + Product 3 Net Revenue + Product 4 Net Revenue) - ($12600 + $5000 + $3000 + $4000)

Profit = $19100 - $25600

Profit = $6500/month

So, our profit per month when we are the only worker is $6500.

Exercise 1(10)

To improve productivity, we could consider various options such as hiring more workers, improving the efficiency of our resources, or streamlining our procedures. Let's assume that by implementing these changes, we can reduce the processing time for each product at each resource by 20%, while keeping the total number of working hours per day the same.

Let's first recalculate the bottleneck resource and the actual flow rates for each product based on the new processing times. We can find the new processing time for each product at each resource by reducing the old processing time by 20%.

Let's identify the resource that has the longest processing time for any of the products with the new processing times. The longest processing time is now 2.0 hours per unit for Resource 1 for Product 1, instead of 2.5 hours per unit. Therefore, Resource 1 is still the bottleneck.

Let's calculate the actual flow rates of each product based on the new processing times. The formula is the same as before, except now we use the new processing times:

• Product 1: Actual flow rate = Demand / (Processing time per unit at bottleneck resource * Number of working hours per day * Number of working days per month) Actual flow rate = 80 units / (2 hours / unit * 10 hours / day * 25 days / month) = 38.46 units per day
• Product 2: Actual flow rate = Demand / (Processing time per unit at bottleneck resource * Number of working hours per day * Number of working days per month) Actual flow rate = 100 units / (1.6 hours / unit * 10 hours / day * 25 days / month) = 93.75 units per day
• Product 3: Actual flow rate = Demand / (Processing time per unit at bottleneck resource * Number of working hours per day * Number of working days per month) Actual flow rate = 120 units / (1.6 hours / unit * 10 hours / day * 25 days / month) = 122.5 units per day
• Product 4: Actual flow rate = Demand / (Processing time per unit at bottleneck resource * Number of working hours per day * Number of working days per month) Actual flow rate = 100 units / (0.4 hours / unit * 10 hours / day * 25 days / month) = 400 units per day

Let's calculate the profit per month with the new actual flow rates:

Profit = (Product 1 Net Revenue + Product 2 Net Revenue + Product 3 Net Revenue + Product 4 Net Revenue) - ($12600 + $5000 + $3000 + $40