consider the following linear programming problem: maximize 25x + 35y subject to

Question

consider the following linear programming problem:

maximize 25x + 35y

subject to: x + y <76

9x+8y<550

2x+3y>476

x,y>0

this is a special case of a linear programming problem in which

there is no feasible solution.

there is a redundant constraint.

there are multiple optimal solutions.

this cannot be solved graphically.

None of the above

there is no feasible solution.

there is a redundant constraint.

there are multiple optimal solutions.

this cannot be solved graphically.

None of the above

Explanation / Answer

In this problem option A is correct since there is no feasible region here in the first quadrant

when we find the common region for feasible region in first quadrant the equation gives an unbounded egion above the line 2x+3y=276

and the other two lines x+y<76 and 9x+8y <550 give a small bounded region below the line 9x+8y =550

but no common point of intersection, so no feasible point. so no solution

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