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Given an annual capital investment of RM x million, along with the employment of y million unskilled labour hours and z million skilled labour hours per year, the annual sugar production output (in tonnes) of a sugarcane mill can be modelled by the function Q(x, y, z)= -en= 16 100 in which the values of x, y, and z should adhere to the budget constraint of 2x² + y² + 2z² = 21 Apply both the D-test method AND the method of Lagrange multipliers to determine the

Given an annual capital investment of RM x million, along with the employment of y million unskilled labour hours and z million skilled labour hours per year, the annual sugar production output (in tonnes) of a sugarcane mill can be modelled by the function Q(x, y, z)= -en= 16 100 in which the values of x, y, and z should adhere to the budget constraint of 2x² + y² + 2z² = 21 Apply both the D-test method AND the method of Lagrange multipliers to determine the

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Given an annual capital investment of RM x million, along with the employment of y million unskilled labour hours and z million skilled labour hours per year, the annual sugar production output (in tonnes) of a sugarcane mill can be modelled by the function 16 Q(x, y, z) = - -enz 100 in which the values of x, y, and z should adhere to the budget constraint of 2x² + y² + 2z² = 21 Apply both the D-test method AND the method of Lagrange multipliers to determine the optimal allocation of capital investment and the most effective utilization of unskilled and skilled labour force to maximize sugar production. Then, compare and comment on the two methods used.
Transcribed Image Text:Given an annual capital investment of RM x million, along with the employment of y million unskilled labour hours and z million skilled labour hours per year, the annual sugar production output (in tonnes) of a sugarcane mill can be modelled by the function 16 Q(x, y, z) = - -enz 100 in which the values of x, y, and z should adhere to the budget constraint of 2x² + y² + 2z² = 21 Apply both the D-test method AND the method of Lagrange multipliers to determine the optimal allocation of capital investment and the most effective utilization of unskilled and skilled labour force to maximize sugar production. Then, compare and comment on the two methods used.
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