$(15$ marks$)$ The management team for Frank's Fine Furniture is considering two locations for a plant to manufacture wooden tables. The fixed setup costs for both plants are identical.

Plant A can produce $100$ tables per week. The plant works one $7$ hour shift per day with $8$ staff. The plant works $5$ days per week. The average wage is $$24$ per hour. The plant would use $700$ units of maple and can buy maple at $$12$ per unit. Based on location and staffing levels, the plant would be assigned an overhead allocation of $$1000$ per week.

Plant B can produce $75$ tables per week. The plant works one $8$ hour shift per day with $9$ staff. The plant works $5$ days per week. The average wage is $$19$ per hour. The plant would use $650$ units of maple to make the tables and can buy maple at $$10$ per unit. Based on location and staffing levels, the plant would be assigned an overhead allocation of $$1,700$ per week.

a$)$ What is the total cost of production for a week at each plant? What is the cost per table? What is the labour cost per table?

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?

Operations Management, FARE$*3310-$ Winter $25$: Assignment $1$

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$\text{'}$s manager believes he can increase labour productivity per dollar by $10\%$ by increasing wages to $$26$ per hour. How many tables can they now make in a week? What is the total labour cost per table and total cost per table? How much have each improved in percent?