$7-31$ Consider the following LP problem: Maximize profit$=5$X$+6$Y subject to$2$X$+$Y$<=120,2$X$+3$Y$<=240$X$,$Y$>=0$ What is the optimal solution to this problem? Solve it graphically. If a technical breakthrough occurred that raised the profit per unit of X to $$8,$ would this affect the optimal solution? Instead of an increase in the profit coefficient X to $$8,$ suppose that profit was overestimated and should only have been $$3.$ Does this change the optimal solution? $7-32$ Consider the LP formulation given in Problem $7-31.$ If the second constraint is changed from $2$X $+3$Y$<=2402$X $+3$Y$<=240$ to $2$X$+4$Y$<=240,2$X$+4$Y$<=240,$ what effect will this have on the optimal solution?