In the original or primal problem statement, the goal is to maximize profits, and the (primal) objective function is
The dual problem goal is to minimize implicit values or shadow prices for the firm's resources. Defining VA, VB, and VC as the shadow prices for inputs A, B, and C, respectively, and n* as the total implicit value of the firm's fixed resources, the dual objective function (the dual) is
Because the firm has 32 units of A, the total implicit value of input A is 32 times A's shadow price, or 32 VA. If VA, or input A's shadow price, is found to be $1.50 when the dual equations are solved, the implicit value of A is $48 (= 32 X $1.50). Inputs B and C are handled in the same way.
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