math - Eliminate a redundant equation from a linear programming -

i asked re-write linear programming question equation less.

max 7x1+5x2 

s.t :

4x1+3x2 <= 2400 2x1+0.5x2 <= 750 x1 >= 100 x1,x2 >= 0 

what did used simplex method , found maximum profit 4030 x1 = 100 , x2=666. can use , to obtain maximum profit, x1 has 100, third equation extra?

since consider simple 2-dimensional problem, can solve graphically. first note gradient of objective function is

∇f_obj = (7, 5) 

from points , onwards, we'll denote variable x1 x, , x2 y.

the constraints describe polytope (a) below, , level curves objective function given in (b) (brighter contour: increased objective function value).

the optimal value marked red dot in (b) above, (x^*, y^*) = (262.5, 450).

it's apparent inequality constraints 4x+3y <= 2400 , 2x+0.5y <= 750 both active, optimum given in intersection of these two.

the constraint x >= 100 (x1 >= 100), is, however, not active, , hence redundant.