Question

Charles Lackey operates a bakery in Idaho​ Falls, Idaho. Because of its excellent product and excellent​ location, demand has increased by 35 ​% in the last year. On far too many​ occasions, customers have not been able to purchase the bread of their choice. Because of the size of the​ store, no new ovens can be added. At a staff​ meeting, one employee suggested ways to load the ovens differently so that more loaves of bread can be baked at one time. This new process will require that the ovens be loaded by​ hand, requiring additional manpower. This is the only production change that will be made in order to meet the increased demand. The bakery currently makes 1500 loaves per month. Employees are paid ​$8 per hour. In addition to the labor​ cost, Charles also has a constant utility cost per month of ​$850 and a per loaf ingredient cost of ​$0.50.

Part 2
Current multifactor productivity for 640 work hours per month​ = 0.223 ​loaves/dollar ​(round your response to three decimal​ places).
Part 3
After increasing the number of work hours to 864 hours per month​, the multifactor productivity​ =? loaves/dollar enter your response here ​loaves/dollar ​(round your response to three decimal​ places).

Answer 1

Part 2: Current multifactor productivity for 640 work hours per month

To calculate the current multifactor productivity, we need to consider the total output (loaves of bread) and the total cost (including labor, utility, and ingredient costs).

1. Total output = 1500 loaves per month
2. Total cost = Labor cost + Utility cost + Ingredient cost
Labor cost = 640 work hours * $8/hour
Utility cost = $850
Ingredient cost per loaf = $0.50

Now, calculate the total cost:

Labor cost = 640 hours * $8/hour = $5,120
Utility cost = $850
Ingredient cost per loaf = $0.50

Total cost = $5,120 + $850 + ($0.50 * 1500) = $5,120 + $850 + $750 = $6,720

Now, calculate the current multifactor productivity:

Multifactor Productivity = Total Output / Total Cost
Multifactor Productivity = 1500 / $6,720 ≈ 0.223 (rounded to three decimal places)

So, the current multifactor productivity is approximately 0.223 loaves per dollar.

Part 3: After increasing the number of work hours to 864 hours per month

With 864 work hours per month, we'll calculate the new multifactor productivity. The total cost will change due to increased labor costs, but other costs remain the same.

1. Total output = 1500 loaves per month
2. Total cost = Labor cost + Utility cost + Ingredient cost

New labor cost = 864 hours * $8/hour
Utility cost = $850
Ingredient cost per loaf = $0.50

Now, calculate the new total cost:

New labor cost = 864 hours * $8/hour = $6,912

Total cost = New labor cost + Utility cost + Ingredient cost
Total cost = $6,912 + $850 + ($0.50 * 1500) = $6,912 + $850 + $750 = $7,512

Now, calculate the new multifactor productivity:

Multifactor Productivity = Total Output / Total Cost
Multifactor Productivity = 1500 / $7,512 ≈ 0.199 (rounded to three decimal places)

So, after increasing the number of work hours to 864 hours per month, the new multifactor productivity is approximately 0.199 loaves per dollar.