Question

1) (20 points) The management team for Buddy's Bats is considering two locations for a plant to manufacture wooden baseball bats. The plant will produce 500 bats per week. The fixed setup costs for both plants are identical. Plant A can produce 500 bats per week. The plant works one 8 hour shift per day with 5 staff. The plant works 5 days per week. The average wage is $25 per hour. The plant would use 600 units of maple and can buy maple at $5 per unit. Based on location and staffing levels, the plant would be assigned an overhead allocation of $1000 per week. Plant B can produce 500 bats per week. The plant works one 8 hour shift per day with 7 staff. The plant works 5 days per week. The average wage is $20 per hour. The plant would use 625 units of maple to make the bats and can buy maple at $4 per unit. Based on location and staffing levels, the plant would be assigned an overhead allocation of $1,500 per week. a) What is the total cost of production for a week at each plant? What is the cost per bat? What is the labour cost per bat? b) Calculate and compare the labour productivity of the two options. Which one is better? c) Calculate and compare the multi-factor (labour, input and overhead) productivity of the two options. Which location is preferred? d) Give two other factors that the management team should consider before choosing a location (there may be more than 2 but only 2 are required). e) Plant A's manager believes he can increase labour productivity by 10% by increasing wages to $26 per hour. How many bats can they now make in a week? What is the total labour cost per bat and total cost per bat? How much have each improved?

Answer 1

a)

At plant A,

Total cost of production = Material(maple) cost+labour wage cost + overhead cost

=600*5+5*5*8*25+1000 = 9000

Cost per bat = 9000/500 = 18

labour cost per bat = (5*5*8*25)/500 = 10

At plant B,

Total cost of production = Material(maple) cost+labour wage cost + overhead cost

=625*4+7*5*8*20+1500 = 9600

Cost per bat = 9600/500 = 19.2

labour cost per bat = (7*5*8*20)/500 = 11.2

b) Labour productivity at plant A = Output/labour cost = 500/(5*5*8*25) = 0.1

Labour productivity at plant B = Output/labour cost = 500/(7*5*8*20) = 0.089285714

Plant A is better

c)

Multi-factor productivity at plant A = Output/Total cost = 500/(600*5+5*5*8*25+1000) = 0.055555556

Multi-factor productivity at plant B = Output/Total cost = 500/(625*4+7*5*8*20+1500) = 0.052083333

Plant A is better

d)

Two other factors that should be considered before choosing a location :

1. Transport facilities
2. Availability of Raw materials

e.

after 10% increase, labour productivity at plant A => 0.1*1.1 = 0.11

Now, output/(5*5*8*26) = 0.11

or, output = 0.11*5*5*8*26 = 572

Now, they can make 572 bats per week

Total labour cost per bat = (5*5*8*26)/572 = 9.090909091
Total cost per bat = (600*5+5*5*8*26+1000)/572 = 16.08391608

Total labour cost per bat has improved by 10-9.090909091 = 0.909090909

Total cost per bat has improved by 18-16.08391608 = 1.91608392