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- https://math.libretexts.org/Under_Construction/Purgatory/Remixer_University/Username%3A_pseeburger/MATH_223_Calculus_III/Chapter_13%3A_Functions_of_Multiple_Variables_and_Partial_Derivatives/13.9%3A_Constrained_OptimizationSince the cost of the material in the bottom of the box is twice the cost of the materials in the rest of the box, we'll need to account for this in the constraint. Postal Service states that the girt...Since the cost of the material in the bottom of the box is twice the cost of the materials in the rest of the box, we'll need to account for this in the constraint. Postal Service states that the girth plus the length of Standard Post Package must not exceed 130''. Given a rectangular box, the "length'' is the longest side, and the "girth'' is twice the sum of the width and the height.
- https://math.libretexts.org/Courses/Oxnard_College/Multivariable_Calculus/02%3A_Functions_of_Multiple_Variables_and_Partial_Derivatives/2.10%3A_Constrained_OptimizationSince the cost of the material in the bottom of the box is twice the cost of the materials in the rest of the box, we'll need to account for this in the constraint. Postal Service states that the girt...Since the cost of the material in the bottom of the box is twice the cost of the materials in the rest of the box, we'll need to account for this in the constraint. Postal Service states that the girth plus the length of Standard Post Package must not exceed 130''. Given a rectangular box, the "length'' is the longest side, and the "girth'' is twice the sum of the width and the height.
- https://math.libretexts.org/Courses/Al_Akhawayn_University/MTH2301_Multivariable_Calculus/13%3A_Functions_of_Multiple_Variables_and_Partial_Derivatives/13.09%3A_Applications_of_Optimization_Constrained_Optimization_and_Absolute_ExtremaTo find the minimum value of this function (and the corresponding values of the parameters \(a, b, c,\) and \(d\) needed for the best fit cubic regression model), we need to find the critical point of...To find the minimum value of this function (and the corresponding values of the parameters \(a, b, c,\) and \(d\) needed for the best fit cubic regression model), we need to find the critical point of this function. (Yes, even for a function of four variables!) To begin this process, we find the first partial derivatives of this function with respect to each of the parameters \(a, b, c,\) and \(d\).
- https://math.libretexts.org/Courses/El_Centro_College/MATH_2514_Calculus_III/Chapter_13%3A_Functions_of_Multiple_Variables_and_Partial_Derivatives/13.9%3A_Constrained_OptimizationSince the cost of the material in the bottom of the box is twice the cost of the materials in the rest of the box, we'll need to account for this in the constraint. Postal Service states that the girt...Since the cost of the material in the bottom of the box is twice the cost of the materials in the rest of the box, we'll need to account for this in the constraint. Postal Service states that the girth plus the length of Standard Post Package must not exceed 130''. Given a rectangular box, the "length'' is the longest side, and the "girth'' is twice the sum of the width and the height.
- https://math.libretexts.org/Courses/Coastline_College/Math_C280%3A_Calculus_III_(Everett)/03%3A_Functions_of_Multiple_Variables_and_Partial_Derivatives/3.10%3A_Constrained_OptimizationSince the cost of the material in the bottom of the box is twice the cost of the materials in the rest of the box, we'll need to account for this in the constraint. Postal Service states that the girt...Since the cost of the material in the bottom of the box is twice the cost of the materials in the rest of the box, we'll need to account for this in the constraint. Postal Service states that the girth plus the length of Standard Post Package must not exceed 130''. Given a rectangular box, the "length'' is the longest side, and the "girth'' is twice the sum of the width and the height.
- https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Active_Calculus_(Boelkins_et_al.)/10%3A_Derivatives_of_Multivariable_Functions/10.08%3A_Constrained_Optimization-_Lagrange_MultipliersSome optimization problems involve maximizing or minimizing a quantity subject to an external constraint. In these cases the extreme values frequently won't occur at the points where the gradient is z...Some optimization problems involve maximizing or minimizing a quantity subject to an external constraint. In these cases the extreme values frequently won't occur at the points where the gradient is zero, but rather at other points that satisfy an important geometric condition. These problems are often called constrained optimization problems and can be solved with the method of Lagrange Multipliers, which we study in this section.
- https://math.libretexts.org/Courses/Coastline_College/Math_C280%3A_Calculus_III_(Tran)/03%3A_Functions_of_Multiple_Variables_and_Partial_Derivatives/3.10%3A_Constrained_OptimizationSince the cost of the material in the bottom of the box is twice the cost of the materials in the rest of the box, we'll need to account for this in the constraint. Postal Service states that the girt...Since the cost of the material in the bottom of the box is twice the cost of the materials in the rest of the box, we'll need to account for this in the constraint. Postal Service states that the girth plus the length of Standard Post Package must not exceed 130''. Given a rectangular box, the "length'' is the longest side, and the "girth'' is twice the sum of the width and the height.
- https://math.libretexts.org/Courses/Monroe_Community_College/MTH_212_Calculus_III/Chapter_13%3A_Functions_of_Multiple_Variables_and_Partial_Derivatives/13.9%3A_Applications_of_Optimization_Constrained_Optimization_and_Absolute_ExtremaTo find the minimum value of this function (and the corresponding values of the parameters \(a, b, c,\) and \(d\) needed for the best fit cubic regression model), we need to find the critical point of...To find the minimum value of this function (and the corresponding values of the parameters \(a, b, c,\) and \(d\) needed for the best fit cubic regression model), we need to find the critical point of this function. (Yes, even for a function of four variables!) To begin this process, we find the first partial derivatives of this function with respect to each of the parameters \(a, b, c,\) and \(d\).
