1. **State the problem:** We need to apportion the expenses of service departments S1 and S2 to production departments P1 and P2 and also between themselves using the Simultaneous Equation Method. 2. **Given data:** - Expenses: P1 = 51837, P2 = 12163, S1 = 40000, S2 = 16000 - Apportionment percentages: - S1 to P1 = 50%, P2 = 40%, S2 = 10% - S2 to P1 = 30%, P2 = 50%, S1 = 20% 3. **Define variables:** Let $x$ = total cost of S1 after apportionment Let $y$ = total cost of S2 after apportionment 4. **Form simultaneous equations:** - For S1: $$x = 40000 + 0.2y$$ - For S2: $$y = 16000 + 0.1x$$ 5. **Solve the equations:** Substitute $y$ from second into first: $$x = 40000 + 0.2(16000 + 0.1x) = 40000 + 3200 + 0.02x = 43200 + 0.02x$$ Rearranged: $$x - 0.02x = 43200$$ $$0.98x = 43200$$ $$x = \frac{43200}{0.98} = 44081.63$$ Now find $y$: $$y = 16000 + 0.1(44081.63) = 16000 + 4408.16 = 20408.16$$ 6. **Apportion costs to P1 and P2:** - From S1 ($x = 44081.63$): - To P1: $50\% \times 44081.63 = 22040.82$ - To P2: $40\% \times 44081.63 = 17632.65$ - To S2: $10\% \times 44081.63 = 4408.16$ - From S2 ($y = 20408.16$): - To P1: $30\% \times 20408.16 = 6122.45$ - To P2: $50\% \times 20408.16 = 10204.08$ - To S1: $20\% \times 20408.16 = 4081.63$ 7. **Calculate total expenses for P1 and P2:** - P1 total = Original P1 + from S1 + from S2 = $51837 + 22040.82 + 6122.45 = 79999.27$ - P2 total = Original P2 + from S1 + from S2 = $12163 + 17632.65 + 10204.08 = 39999.73$ **Final answer:** - Total cost of S1 after apportionment: $44081.63$ - Total cost of S2 after apportionment: $20408.16$ - Total cost for P1: $79999.27$ - Total cost for P2: $39999.73$