Consider the following: $$ \begin{align} \text{Maximize}&\enspace 1.04x_4 + 1.09x_9 + 1.15x_{11}\\ \text{subject to}&\enspace x_1+x_6=5000\\ &x_2+x_7+x_{10}=1.04x_1\\ &x_3+x_8+x_{11}=1.04x_2+1.09x_6\\ &x_4+x_9=1.04x_3+1.09x_7\\ &x_5=1.04x_4+1.09x_8+1.15x_{10}\\ &x_1,\dots,x_{11}\geq 0 \end{align} $$ My approach to solving this problem is to transform each equality into an inequality, e.g. the first constraint is equivalent to $$x_1+x_6\leq5000$$ $$-x_1-x_6\leq5000$$ I would then do this for the rest. However, the other constraints have variables on the the right hand side of the "$=$", does this mean I must subtract them, making those constraints less than or equal to zero?
Also, if I were to do this, I would only have $10$ constraints but there is $11$ variables. Isn't this a problem?