$1.(50$ Points$)$ Chapter $7-$Linear ProgrammingA company manufactures two products, A and B$.$ The profit per unit for A is $$10,$ and for B is $$15.$ Each product requires two types of resources: labor end material. The company has $300$ hours of labor and $400$ pounds of material available. Product A requires $5$ hours of labor and $10$ pounds of material per unit, while Product B requires $10$ hours of labor and $5$ pounds of material per unit.Formulate the Linear Programming $($LP$)$ model to maximize profit.Solve graphically to find the optimal solution$\mathrm{.}2.(40$ Points$)$ Chapter $4-$Decision AnalysisA decision maker faces three decision alternatives: A$1,$ A$2,$ and A$3.$ The states of nature are S$1,$ S$2,$ and S$3.$ The payoff table is as follows:Decision Alternative S$1$ S$2$ S$3$A$1304050205060502030$A$2$A$3$a$)$ Identify the optimal decision using the maximax, maximin, and minimax regret criteria.b$)$ Calculate the expected value for each alternative assuming probabilities of $0\mathrm{.}3$ for S$1,0\mathrm{.}5$ for S$2,$ and $0\mathrm{.}2$ for S$3\mathrm{.}3.(35$ Points$)$ Chapter $7-$ Linear ProgrammingA company produces two products, X and Y$,$ with a goal to minimize costs. The production of X costs $$12$ per unit, and the production of Y costs $$10$ per unit. The company needs to meet the following constraints:At least $100$ units of X and Y combined.At least $60$ units of X$.$At least $40$ units of Y$.$Formulate the Linear Programming model for this problem and solve it graphically to determine the optimal production levels.