I'm trying to solve a linear programming problem using LINGO software. The textbook gives the answers in the back, so I know I have the below constraints right, but when I enter them into LINGO and solve, I don't get the right answers. The answers should be: X1 = 500, X2 = 300, X3 = 200. Cost: 550. Can anyone point out what I've done/entered wrong?

Max 0.50x1 + .70x2 + .45x3

s.t.

10x2 - 15x3 >= 0

6x1 + 8x2 - 5x3 >= 0

x1 <= 500

x2 <= 600

x3 <= 400

x1 + x2 + x3 = 1000

x1, x2, x3 >= 0

I entered this problem in LINGO like this:

! MAXIMIZE PROFIT;

MAX = 0.50*X1 + 0.70*X2 + 0.45*X3;

!MATERIAL CONSTRAINT 1;

X1 + X2 + X3 = 1000;

!MATERIAL CONSTRAINT 2;

X1 <= 500;

!MATERIAL CONSTRAINT 3;

X2 <= 600;

!MATERIAL CONSTRAINT 4;

X3 <= 400;

!MATERIAL CONSTRAINT 5;

10*X2 - 15*X3 >= 0;

!MATERIAL CONSTRAINT 6;

6*X1 + 8*X2 - 5*X3 >= 0;