Question

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1. In a large metropolitan area, 25% of the commuters currently use the public transportation system, whereas the remaining 75% commute via automobile. The city has recently revitalized and expanded its public transportation system. It is expected that 6 months from now 30% of those who are now commuting to work via automobile will switch to public transportation, and 70% will continue to commute via automobile. At the same time, it is expected that 20% of those now using public transportation will commute via automobile and 80% will continue to use public transportation.

(a) Construct the transition matrix for the Markov chain that describes the change in the mode of transportation used by these commuters.

			P              A
T	=	P A

(b) Find the initial distribution vector for this Markov chain.

X0

=

(c) What percentage of the commuters are expected to use public transportation 6 months from now? (Round your answer to the nearest percent.)
%_______

2.

Solve the system of linear equations using the Gauss-Jordan elimination method.

2x	+	2y	+	z	=	8
x			+	z	=	3
		4y	−	3z	=	16

(x, y, z) = __________

3.Solve the linear programming problem by the method of corners.

Maximize	P = 4x + 7y
subject to	x	+	y	≤	10
	3x	+	y	≥	12
	−2x	+	3y	≥	9
	x ≥ 0, y ≥ 0

The maximum is P =__________ at (x, y) = __________.

Answer 1

Problem in answer then comment below.. i will help you

By rules and regulations we are allow to do only one question at a time..so i do only question 3rf.

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please thumbs up for this solution..thanks..

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Maximize 4x, +7X2 subject to X1 + X2 = 10 3x, + X2 12 - 2X1 + 3x2 > 9 #3 FACTORY RESTRICTIONS EQUATIONS Maximize 4x, +7X2 subject to = 10 X1 + X2 + X3 3X1 + X2 - 2x2 + 3x2 -XA + Y1 = 12 - X5 + y2 = 9 #4 SIMPLEX TABLE 1 X2 X3 X4 y1 Y2 b t X1 1 X5 0 X3 1 0 0 0 10 10 1 1 У1 3 0 -1 0 1 0 12 12 Y2 -2 3 0 0 -1 0 1 9 3 N -4 -7 0 0 0 0 0 0 'N -1 -4 0 1 1 0 0 -21

#6 SIMPLEX TABLE 3 X1 X2 X3 X4 X5 y1 y2 b t X3 5/3 0 1 0 1/3 0 -1/3 7 21/5 y1 11/3 0 0 -1 1/3 1 -1/3 9 27/11 -2/3 1 0 0 -1/3 0 1/3 3 z -26/3 0 0 0 -7/3 0 7/3 21 z -11/3 0 0 1 -1/3 0 4/3 -9 #7 SIMPLEX TABLE 4 X1 X2 X3 X4 X5 y1 y2 b t X30 0 1 5/11 2/11 -5/11 -2/11 32/11 32/5 X1 1 0 0 -3/11 1/11 3/11 -1/11 27/11 X2 0 1 0 -2/11 -3/11 2/11 3/11 51/11 z 0 0 0 -26/11 -17/11 26/11 17/11 465/11 z' 0 0 0 0 0 1 1 0 #8 SIMPLEX TABLE 5 X1 X2 X3 X4 X5 b t X4 0 0 11/5 1 2/5 32/5 16 X1 1 0 3/5 0 1/5 21/5 21 X2 0 1 2/5 0 -1/5 29/5 z 0 0 26/5 0 -3/5 287/5 #9 SIMPLEX TABLE 6 X1 X2 X3 X4 X5 b X5 0 0 11/2 5/2 1 16 X1 1 0 -1/2 -1/2 0 1 X2 0 1 3/2 1/2 0 9 z 0 0 17/2 3/2 0 67 SOLUTION x(5) = (1,9,0,0,16) z(5) = 67

so , max P = 67 at (x,y) = (1,9)