Could you please explain the following question, the textbook gave the answer below, but I am not sure how they get there. Q.a? 15.21 The economy of Northern Saskatchewan is in equilibrium when the system ofequations2xz + xy + z – 2/z = 11xyz = 6is satisfied. One solution of this set of equations is x =Northern Saskatchewan is in equilibrium at this point. Suppose that the primeminister discovers that the variable z (output of beaver pelts) can be conrolled bysimple decree.a) If the prime minister raises z to 1.1, use calculus to estimate the change in x and3, у2, z1, andу.b) If x were in the control of the prime minister and not y or z, explain why youcannot use this method to estimate the effect of reducing x from 3 to 2.95. 15.21 a)(2z + y) dx + x dy + (2x + 1 –z-1/2) dz = 0(yz) dx + (xz) dy + (xy)dz = 0,74MATHEMATICS FOR ECONOMISTSor4 dx + 3 dy + 6(0.1) = 02 dx + 3 dy + 6(0.1) = 0.O and dySubtracting yields dxy = 1.8.-0.6/3— —0.2. So, х ~ 3,

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Description: Could you please explain the following question, the textbook gave the answer below, but I am not sure how they get there. Q.a? 15.21 The economy of Northern Saskatchewan is in equilibrium when the system ofequations2xz + xy + z – 2/z = 11xyz = 6is s

Given:- 2xz+xy+z-2z=11------1 xyz=6 ------2 (a) Express x and y as a function of…

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uations 2xz + xy + z – 2z = 11 xyz = 6 satisfied. One solution of this set of equations is x = rthern Saskatchewan is in equilibrium at this point. Suppose that the prim nister discovers that the variable z (output of beaver pelts) can be conrolled bị 3, у %3D 2,z 1, an %3D

uations 2xz + xy + z – 2z = 11 xyz = 6 satisfied. One solution of this set of equations is x = rthern Saskatchewan is in equilibrium at this point. Suppose that the prim nister discovers that the variable z (output of beaver pelts) can be conrolled bị 3, у %3D 2,z 1, an %3D

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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Could you please explain the following question, the textbook gave the answer below, but I am not sure how they get there. Q.a?

15.21 The economy of Northern Saskatchewan is in equilibrium when the system of
equations
2xz + xy + z – 2/z = 11
xyz = 6
is satisfied. One solution of this set of equations is x =
Northern Saskatchewan is in equilibrium at this point. Suppose that the prime
minister discovers that the variable z (output of beaver pelts) can be conrolled by
simple decree.
a) If the prime minister raises z to 1.1, use calculus to estimate the change in x and
3, у
2, z
1, and
у.
b) If x were in the control of the prime minister and not y or z, explain why you
cannot use this method to estimate the effect of reducing x from 3 to 2.95.

15.21 a)
(2z + y) dx + x dy + (2x + 1 –z-1/2) dz = 0
(yz) dx + (xz) dy + (xy)
dz = 0,
74
MATHEMATICS FOR ECONOMISTS
or
4 dx + 3 dy + 6(0.1) = 0
2 dx + 3 dy + 6(0.1) = 0.
O and dy
Subtracting yields dx
y = 1.8.
-0.6/3
— —0.2. So, х ~ 3,

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