# Solving linear Programming problem with simplex method.

I have tried this question but can't come up with a maximization answer. I am not certain where I am wrong but I think my equations have an issue, you can't take look at them below the question. The questions states, An investor has to invest in an economy and has three options to invest in: banking, insurance and manufacturing. The return on investment is 20%, 25% and 15% respectively. The president said that he must invest the investment in banking should not exceed twice the total investment in insurance and manufacturing by more than 3 million dollars. At the same time not less than 30% of the investment should be in manufacturing. If the total money available to the investor is 18 million dollars.
a) Formulate his problem as an LP problem
b) Use the simplex table to calculate the maximum profit he can make.
NB: Hint: Let the money, in million dollars invested in banking be $$x_1$$ , in insurance be $$x_2$$ and in manufacturing be $$x_3$$ .

In my solution, i managed to come up with my objective function as $$x_1 + x_2 + x_3 = 18$$ and with the constraints I came up with;

(x1 <= x2)....eqn1-(president said that he must invest the investment in banking should not exceed twice the total investment in insurance)

(x1 + 3 <= x3)....eqn2-(manufacturing by more than 3 million dollars)

(x3 >= (30% * 18million))...eqn3-(At the same time not less than 30% of the investment should be in manufacturing.)

From the equations i started iterating and stuff isen't just adding up somewhere. SOMEONE HELP.

The objective function you are using is incorrect. You want to maximise the profit, which you can formulate as $$0.2x_{1} + 0.25x_{2} + 0.15x_{3}$$. The equation you are currently using as the objective is actually another constraint.