1. **Problem:** Find the selling price for Trial 1 using the random number 81. - Selling Price probabilities: - Sh 10: 0.3 (0-30) - Sh 15: 0.3 (31-60) - Sh 10: 0.2 (61-80) - Sh 70: 0.2 (81-100) - Since 81 falls in 81-100, selling price = Sh 70. 2. **Problem:** Find the unit variable cost for Trial 3 using random number 36. - Unit Variable Cost probabilities: - Sh 6: 0.1 (0-10) - Sh 8: 0.3 (11-40) - Sh 10: 0.3 (41-70) - Sh 9: 0.3 (71-100) - 36 falls in 11-40, so cost = Sh 8. 3. **Problem:** Determine units demanded in Trial 2 using random number 10. - Sales Units demand probabilities: - 1000: 0.2 (0-20) - 3000: 0.2 (21-40) - 2000: 0.2 (41-60) - 6000: 0.4 (61-100) - 10 falls in 0-20, units demanded = 1000. 4. **Problem:** Compute profit for Trial 4. - Trial 4 random numbers: - Selling Price: 4 (0-30 Sh 10) - Unit Cost: 29 (11-40 Sh 8) - Units Demand: 23 (21-40 3000 units) - Profit formula: $$\text{Profit} = (\text{Selling Price} - \text{Unit Cost}) \times \text{Units Demand}$$ - Calculate: $$(10 - 8) \times 3000 = 2 \times 3000 = 6000$$ 5. **Problem:** Selling price in Trial 7 with random number 2. - 2 falls in 0-30, selling price = Sh 10. 6. **Problem:** Units demanded in Trial 8 with random number 39. - 39 falls in 21-40, units demanded = 3000. 7. **Problem:** Unit variable cost in Trial 10 with random number 11. - 11 falls in 11-40, cost = Sh 8. 8. **Problem:** Compute profit for Trial 6. - Trial 6 random numbers: - Selling Price: 77 (61-80 Sh 10) - Unit Cost: 9 (0-10 Sh 6) - Units Demand: 78 (61-100 6000 units) - Profit: $$(10 - 6) \times 6000 = 4 \times 6000 = 24000$$ 9. **Problem:** Units demanded in Trial 9 with random number 5. - 5 falls in 0-20, units demanded = 1000. 10. **Problem:** Compute average profit across all 10 trials. - Calculate each trial's selling price, unit cost, units demand, then profit: |Trial|SP Rand|SP|UC Rand|UC|UD Rand|UD|Profit| |---|---|---|---|---|---|---|---| |1|81|70|1|6|99|6000|$(70-6)\times6000=384000$ |2|65|10|53|10|10|1000|$(10-10)\times1000=0$ |3|49|15|36|8|36|2000|$(15-8)\times2000=14000$ |4|4|10|29|8|23|3000|$(10-8)\times3000=6000$ |5|53|10|11|6|25|3000|$(10-6)\times3000=12000$ |6|77|10|9|6|78|6000|$(10-6)\times6000=24000$ |7|2|10|70|9|52|2000|$(10-9)\times2000=2000$ |8|74|10|9|6|39|3000|$(10-6)\times3000=12000$ |9|7|10|6|6|5|1000|$(10-6)\times1000=4000$ |10|29|15|11|8|66|6000|$(15-8)\times6000=42000$ - Sum profits: $384000 + 0 + 14000 + 6000 + 12000 + 24000 + 2000 + 12000 + 4000 + 42000 = 490000$ - Average profit: $$\frac{490000}{10} = 49000$$ **Final answers:** 1. Sh 70 2. Sh 8 3. 1000 units 4. 6000 5. Sh 10 6. 3000 units 7. Sh 8 8. 24000 9. 1000 units 10. 49000