The total cost function of a firm that produces its product on two assembly lines is given as: subject to the constraint: TC= 3X2+6y2 - XY subject to the constraint: X+Y = 20 The problem facing the firm is to determine the least-cost combination of output on assembly lines X and Y subject to the side condition that total output equal 20 units. (A)Use the Lagrangian multiplier method to determine X and Y that lead to the minimization of TC. (B) Verify that the values of X and Y minimize the TC, then Find the TC given the values of X and Y. (C)Interpret the value of the Lagrangian multiplier.
The total cost function of a firm that produces its product on two assembly lines is given as: subject to the constraint: TC= 3X2+6y2 - XY subject to the constraint: X+Y = 20 The problem facing the firm is to determine the least-cost combination of output on assembly lines X and Y subject to the side condition that total output equal 20 units. (A)Use the Lagrangian multiplier method to determine X and Y that lead to the minimization of TC. (B) Verify that the values of X and Y minimize the TC, then Find the TC given the values of X and Y. (C)Interpret the value of the Lagrangian multiplier.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 40E
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The total cost function of a firm that produces its product on two assembly lines is given as:
subject to the constraint:
TC= 3X2+6y2 - XY
subject to the constraint:
X+Y = 20
The problem facing the firm is to determine the least-cost combination of output on assembly lines X and Y subject to the side condition that total output equal 20 units.
(A)Use the Lagrangian multiplier method to determine X and Y that lead to the minimization of TC.
(B) Verify that the values of X and Y minimize the TC, then Find the TC given the values of X and Y.
(C)Interpret the value of the Lagrangian multiplier.
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