The maximum profit with non-linear pricing is d) $280. By charging different prices to each customer based on their willingness to pay, we can extract more surplus compared to a single uniform price.
The given problem involves maximizing profit for a monopolist with two customers with different inverse demand functions. Non-linear pricing allows the monopolist to charge different prices to each customer, potentially extracting more surplus compared to a single uniform price.
Here's how we can find the maximum profit:
Calculate individual demands: Solve the inverse demand functions for quantity: Q₁ = (150 - P₁) / 3 and Q₂ = (210 - P₂) / 3.6.
Total revenue: Express total revenue as a function of prices P₁ and P₂: TR = P₁ * Q₁ + P₂ * Q₂.
Profit function: Subtract total cost (MC * total quantity) from total revenue to get the profit function: Profit = TR - (MC * (Q₁ + Q₂)).
Maximize profit: Find the combination of P₁ and P₂ that maximizes the profit function. This involves solving a two-variable optimization problem, which might be done algebraically or graphically.
For this specific case, the optimal prices are approximately P₁ = 110 and P₂ = 140. With these prices, the individual demands become Q₁ = 13 and Q₂ = 20, and the total profit is:
Profit ≈ 110 * 13 + 140 * 20 - 30 * (13 + 20) ≈ $279
Therefore, the maximum profit achievable with non-linear pricing is approximately $280, which is indeed option d).