3. Consider the following problem: \text { Maximize } \quad Z=2 x_{1}+4 x_{2}-x_{3} subject to 3 x_{2}-x_{3} \leq 30 \quad \text { (resource 1) } 2 x_{1}-x_{2}+x_{3} \leq 10 \quad \text { (resource 2) } 4 x_{1}+2 x_{2}-2 x_{3} \leq 40 \quad \text { (resource 3) } and x1 2 0,x2 2 0,X3 2 0. хI2 0, х220,x1 >x2 > 0,X3 2 0. (a) Work through the simplex method step by step in tabular form to solve the problem. (b) Identify the shadow prices for the three resources and describe their significance.