Exercise $6\mathrm{.}4$ Consider a linear programming problem of the form minimize cjx$1+$c$2$x$2$ coy X$1$ subject to $0$ D F$2$ Di $0$F x$,$ x$220.$ We will develop two different ways of decomposing this problem $262$ Chap. Large scale optimization $($a$)$ Form the dual problem and explain how Dantzig$-$Wolfe decomposition carn be applied to it$.$ What is the structure of the subproblems solved during a typical iteration? $($b$)$ Rewrite the first set of constraints in the form Dix Fiy $2$ b and D$2$x$2+$ F$2>$ b$2,$ together with a constraint relating y$,$ to y$2.$ Discuss how to apply Dantzig$-$Wolfe decomposition and describe the structure of the subproblems solved during a typical iteration