Question

Solve the following problem using both graphical method and Simplex tableau

Maximize f(x,y)=5x+4y subject to 3x+5y<=180 where 28 => x => 0 and 30=> y=>0

Answer 1

Graphical method

Graphical representation of constraints and objective function is following:

Feasible region is the shaded region, bounded by corner points as highlighted on the graph

Corner points are: (28,0), (28,19.2), (10,30), (0,30)

Determine objective function value f(x,y) at each of the corner points:

x	y	f(x,y)
28	0	140
28	19.2	216.8
10	30	170
0	30	120

Maximum objective function value is 216.8 at corner point (28,19.2)

Therefore, optimal solution is:

x = 28

y = 19.2

Objective function value = 5*28+4*19.2

= 216.8

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Simplex tableau