1. **Problem Statement:** Calculate the optimal number of Solar Home Kits to purchase to maximize expected gross profit after advertising in (i) one newspaper and (ii) two newspapers, given demand probabilities and costs. 2. **Given Data:** - Selling price per kit: $245$ - Cost per kit: $105$ - Salvage value per unsold kit: $70$ - Demand levels: $105, 140, 175, 210, 245$ - Probabilities for one newspaper: $0.25, 0.25, 0.2, 0.1, 0.2$ - Probabilities for two newspapers: $0.1, 0.2, 0.3, 0.2, 0.2$ 3. **Formula for Expected Gross Profit:** $$\text{Profit} = \sum \text{Probability}(d) \times \text{Profit at demand } d$$ Where profit at demand $d$ for order quantity $Q$ is: $$\text{Profit} = \text{Revenue} - \text{Cost} + \text{Salvage}\text{ if unsold}$$ Revenue = $245 \times \min(Q, d)$ Cost = $105 \times Q$ Salvage = $70 \times (Q - d)$ if $Q > d$, else 0 4. **Calculate Expected Profit for each order quantity $Q$ in demand levels:** **For (i) One Newspaper:** Calculate expected profit for $Q = 105, 140, 175, 210, 245$ - For $Q=105$: - Demand $d=105$: Profit = $245 \times 105 - 105 \times 105 + 0 = 245 \times 105 - 11025 = 25725 - 11025 = 14700$ - Demand $d=140$: Profit = $245 \times 105 - 105 \times 105 + 0 = 14700$ (since $Q