Suppose r=4.5 and d=135. What is her total optimal profit?

Question

BlackTom AI · Accepted Answer

Here is how to approach the question, given the information provided and noting what is missing to compute a precise answer.

First, restate the data: r = 4.5 and d = 135. The question asks for the total optimal profit, but the specific profit function or business model is not given in the prompt.

Option 1: Compute profit as a straightforward product of two quantities (e.g., revenue per unit times units sold). If we interpret profit as r multiplied by d, we would calculate 4.5 × 135 = 607.5. This is a simple, common interpretation, but it assumes profit per unit is r and that all units sold contribute positively with no fixed costs or nonlinear effects.

Option 2: Consider that the provided answer (2295.0000) might imply a different formula, such as multiplying by an additional factor. To see what would be needed to reach 2295, solve for the missing factor: 2295 ÷ (4.5 × 135) = 2295 ÷ 607.5 ≈ 3.785. This suggests that, under a model where total profit = r × d × factor, the factor would need to be about 3.785. Since that factor isn’t given, this is speculative and indicates a mismatch between the data and the claimed answer.

Option 3: If the problem is about optimizing profit in a market where r is a rate (e.g., price, marginal profit) and d is demand, the total optimal profit could depend on a more complex function (e.g., considering costs, diminishing returns, or a second-order condition). Without the explicit function or constraints (pricing, cost structure, capacity limits), we cannot determine the optimum.

Option 4: Examine potential misinterpretations. Sometimes problems use r as revenue per unit, d as quantity demanded, and total profit as (price − cost) × quantity. If there were a cost per unit, or a fixed cost, those would alter the calculation. None of these are provided here, so any computed value without that context would be guessing.

In summary, with only r = 4.5 and d = 135 and no explicit profit function, cost structure, or optimization constraints, the precise total optimal profit cannot be determined. The calculation 4.5 × 135 = 607.5 is a straightforward interpretation under a simple profit-per-unit model, but it does not account for potential costs or other factors that could yield the given 2295. If the intended model multiplies by an additional factor (about 3.785), you would need to know where that factor comes from (e.g., a multiplier in the profit function, a scaling due to units, or a different interpretation of r or d). Without that context, we can't definitively justify the value 2295.0 as the correct total optimal profit.

COMM_V 190 101-104 2025W1 2025W1 COMM 190 Final Exam - TUE Dec 09 2025 - Requires Respondus LockDown Browser

Suppose r=4.5 and d=135. What is her total optimal profit?

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