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Although similar to the budget constraint in consumer theory, the use of the isocost line pertains to cost-minimization in production, as opposed to utility-maximization.
en.wikipedia.org The isocost line is combined with the isoquant map to determine the optimal production point at any given level of output.
en.wikipedia.org Each straight line segment is an isocost curve showing various amounts of labor and capital whose combined usage would cost a given amount unique to that isocost curve.
en.wikipedia.org A cost-minimizing input bundle is a point on the isoquant for the given "y" that is on the lowest possible isocost line.
en.wikipedia.org The points on an expansion path occur where the firm's isocost curves, each showing fixed total input cost, and its isoquants, each showing a particular level of output, are tangent.
en.wikipedia.org