1. **Problem Statement:** (a) The clothing store owner must decide how many shirts to order (100, 150, 200, or 250) before the season starts. The cost per shirt is 8, unsold shirts are sold at a loss for 12, and returned shirts are rejected at 5. The maximum demand is 500. We use the Expected Monetary Value (EMV) criterion to select the best order quantity and find the Expected Value of Perfect Information (EVPI). (b) Construct the payoff table for ordering decisions. (c) Given fixed production costs for box office sizes (Small 200000, Medium 900000, Large 300000), find the best action using the Expected Opportunity Loss (EOL) criterion. --- 2. **Step 1: Define variables and probabilities** - Order quantities: $Q = \{100, 150, 200, 250\}$ - Cost per shirt: $C = 8$ - Loss on unsold shirt: $L_u = 12$ - Recycle price for returned shirt: $R = 5$ - Demand probabilities (assumed from problem context, not fully specified): - Demand levels: Low, Moderate, High with probabilities $p = \{0.3, 0.45, 0.25\}$ - Demand quantities for products A, B, C given but focus on total demand for shirts. 3. **Step 2: Calculate payoffs for each order quantity and demand level** - Revenue per shirt sold assumed as $S$ (not given, so assume $S = 20$ for calculation example). - For each order quantity $q$ and demand $d$: - Sold shirts = $\min(q, d)$ - Unsold shirts = $\max(0, q - d)$ - Payoff = Revenue from sold shirts $+ R \times$ returned shirts $- C \times q - L_u \times$ unsold shirts 4. **Step 3: Calculate EMV for each order quantity** $$EMV(q) = \sum_{d} p(d) \times \text{Payoff}(q,d)$$ 5. **Step 4: Select order quantity with maximum EMV** 6. **Step 5: Calculate EVPI** - EV with perfect information = $\sum_{d} p(d) \times \max_{q} \text{Payoff}(q,d)$ - EV without perfect information = $\max_{q} EMV(q)$ - EVPI = EV with perfect information $-$ EV without perfect information 7. **Step 6: Construct payoff table (b)** - Rows: Order quantities - Columns: Demand levels - Entries: Payoffs calculated in Step 2 8. **Step 7: EOL criterion (c)** - Calculate regret for each decision and demand: $$Regret(q,d) = \max_{q'} Payoff(q',d) - Payoff(q,d)$$ - Calculate EOL for each $q$: $$EOL(q) = \sum_{d} p(d) \times Regret(q,d)$$ - Choose $q$ with minimum EOL 9. **Summary:** - Use EMV to select order quantity. - Calculate EVPI to measure value of perfect demand knowledge. - Use payoff table to visualize outcomes. - Use EOL to select best action considering regret. **Note:** Specific numerical answers require exact demand probabilities and prices, which are partially missing. The method above guides solving the problem.