1. **Problem Statement:** TechNova Solutions must decide between launching a smart home device immediately or conducting a market trial first, then deciding to launch or cancel based on trial results. 2. **Step 1: Define immediate launch outcomes and probabilities:** - Strong acceptance: Probability $0.40$, Profit ₱600,000 - Moderate acceptance: Probability $0.35$, Profit ₱250,000 - Poor acceptance: Probability $0.25$, Loss ₱150,000 3. **Step 2: Calculate expected monetary value (EMV) if launching immediately:** $$EMV_{immediate} = 0.40 \times 600,000 + 0.35 \times 250,000 + 0.25 \times (-150,000)$$ $$= 240,000 + 87,500 - 37,500 = 290,000$$ 4. **Step 3: Define trial costs and probabilities:** - Trial cost: ₱80,000 (paid upfront) - Trial results probabilities: Favorable $0.55$, Unfavorable $0.45$ 5. **Step 4: Define conditional acceptance probabilities after trial:** - If Favorable: Strong $0.70$, Moderate $0.20$, Poor $0.10$ - If Unfavorable: Strong $0.20$, Moderate $0.40$, Poor $0.40$ 6. **Step 5: Calculate EMV of launching after a Favorable trial:** $$EMV_{Favorable} = 0.70 \times 600,000 + 0.20 \times 250,000 + 0.10 \times (-150,000)$$ $$= 420,000 + 50,000 - 15,000 = 455,000$$ 7. **Step 6: Calculate EMV of launching after an Unfavorable trial:** $$EMV_{Unfavorable} = 0.20 \times 600,000 + 0.40 \times 250,000 + 0.40 \times (-150,000)$$ $$= 120,000 + 100,000 - 60,000 = 160,000$$ 8. **Step 7: Decide whether to launch or cancel after each trial result:** - After Favorable trial: Launch (EMV ₱455,000) vs Cancel (₱0), choose Launch - After Unfavorable trial: Launch (EMV ₱160,000) vs Cancel (₱0), choose Launch 9. **Step 8: Calculate overall EMV if conducting trial then deciding:** $$EMV_{trial} = -80,000 + 0.55 \times 455,000 + 0.45 \times 160,000$$ $$= -80,000 + 250,250 + 72,000 = 242,250$$ 10. **Step 9: Compare EMVs and recommend:** - Launch immediately EMV: ₱290,000 - Conduct trial then decide EMV: ₱242,250 - Cancel EMV: ₱0 **Recommendation:** Launch immediately since it has the highest expected monetary value. 11. **Decision Tree Summary:** - Immediate launch: single chance node with three outcomes and probabilities. - Trial: pay ₱80,000, then chance node for trial result (Favorable/Unfavorable), then decision node to launch or cancel. - Launch outcomes after trial use conditional probabilities. Final answer: Launch immediately with expected profit ₱290,000.