(Solved): d) Make a standard form and canonical form Please answer (a)-(d) in detail In Exercise 1.16 you ...

d) Make a standard form and canonical form

Please answer (a)-(d) in detail

In Exercise 1.16 you modelled the shampoo manufacturing problem as minimize \( z=15 x_{1}+22.5 x_{2} \) subject to \[ \begin{array}{c} 0.2 x_{1}+0.05 x_{2} \geqslant 1 \\ 0.2 x_{1}+0.5 x_{2} \geqslant 3 \\ 0.2 x_{1}+0.3 x_{2} \leqslant 2.5 \\ x_{1}+\quad x_{2} \leqslant 10 \\ x_{1}, x_{2} \geqslant 0 \end{array} \] (a) Solve this model graphically. (b) Deduce the values of the variables \( x_{3}, x_{4}, x_{5} \) and \( x_{6} \) introduced in the solution to Exercise \( 1.16 \) to obtain the canonical form of the model. (c) Interpret your solution as a solution to the original problem.