Question

Cost	Process X	Process Y
Fixed	Rs. 10,000	Rs. 40,000
Variable	Rs. 5/unit	Rs. 2/unit

If the objective is to select a process with the least total cost for a given demand, which one of the following is the most appropriate choice?
1. Below 10,000 units, Process X; Above 10,000 units, Process Y 
2. Below 10,000 units, Process Y; Above 10,000 units, Process X
3. Below 20,000 units, Process X; Above 20,000 units, Process Y
4. Below 20,000 units, Process Y; Above 20,000 units, Process X

Answer 1

Correct Answer - Option 1 : Below 10,000 units, Process X; Above 10,000 units, Process Y 

Concept:

Total Cost of Production (TC) = Fixed Cost + Variable Cost × No. of units.

Calculation:

Let demand be 'x' the number of units at which total cost of production for manufacturing company by process X and by process Y becomes equal.

Total Cost of Production = Fixed Cost + Variable Cost × No. of units.

Total Cost of Production for Process X = 10,000 + 5 x 

and Total Cost of Production for Process Y = 40,000 + 2 x

Equating both process total cost, we get

10000 + 5x = 40000 + 2x

3x = 30000

x = 10000 units

10000 units is the number of units above and below which either one of process will be economical.

If x < 10000, let x = 1000 

⇒ TCx = 10000 + 5 × 1000 = Rs. 15,000  ...for process X

⇒ TCy = 40000 + 2 × 1000 = Rs. 42,000  ...for process Y

∴ TC_x  <  TC_Y

⇒ For no. of units below 10,000 Process X is more preferrable than Process Y.

If x > 10000, let x = 20000 

⇒ TCx = 10000 + 5 × 20000 = Rs. 1,10,000  ...for process X

⇒ TCy = 40000 + 2 × 20000 = Rs. 80,000  ...for process Y

∴ TCx  >  TCY

⇒ For no. of units above 10,000 Process Y is more preferrable than Process X.