A curve that illustrates how the optimal mix of inputs varies with total output is:

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The question asks which curve shows how the optimal mix of inputs changes as total output varies. 
Option 1: The firm’s expansion path. This is the correct concept in production theory; the expansion path traces the least-cost input combinations (input bundles) as output expands, showing how a firm adjusts the mix of capital and labor to produce more efficiently.
Option 2: The total cost curve. This curve plots total cost against output, reflecting overall scale of production, not the specific input mix at different output levels. It doesn’t depict the substitution or combination of inputs.
Option 3: The firm’s opportunity cost. Opportunity cost is a broad concept representing the value of the next best alternative foregone; it is not a curve detailing how input usage changes with output, and it does not specify input combinations.
Option 4: The firm’s profit function. The profit function relates revenue minus costs to output and input choices, but it does not directly illustrate the path of input combinations as output changes. It’s about profitability, not the precise input mix across output levels.

ECON3200001.1251 Pre-class Quiz 6

A curve that illustrates how the optimal mix of inputs varies with total output is:

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