You are asked to solve the following Linear Programming $($LP$)$ problem. Objective: Maximize $\backslash (1\mathrm{.}50\backslash$mathrm$\{$~A$\}+3\mathrm{.}00\backslash$mathrm$\{$~B$\}\backslash ),$ Subject to the following constraints: $-\backslash (3\backslash$mathrm$\{$~A$\}+2\backslash$mathrm$\{$~B$\}\backslash$leq $600\backslash )-\backslash (2\backslash$mathrm$\{$~A$\}+4\backslash$mathrm$\{$~B$\}\backslash$leq $600\backslash )-\backslash (\backslash$mathrm$\{$A$\}+3\backslash$mathrm$\{$~B$\}\backslash$leq $420\backslash )-\backslash (\backslash$mathrm$\{$A$\}\backslash$geq $0\backslash )-\backslash (\backslash$mathrm$\{$B$\}\backslash$geq $0\backslash )$ a$.(15$ points$)$ Graphical Solution $-$ Plot the constraints on the grid provided below. $-$ Clearly identify the feasible region and label its corner points. $-$ Show all calculations and explain how you identified the feasible region and corner points. $-$ Once you complete the graph, copy and paste it as a screenshot $($using PrintScreen$)$ into your report. b$.(20$ points$)$ Analytical Solution $-$ Calculate and report the optimal product mix $($i$.$e$.,$ values of A and B$)$ that maximizes the objective function. $-$ Clearly explain how you arrived at this solution. e$.(15$ points$)$ Excel Solver Solution $-$ Reproduce this problem in Excel and solve it using Excel's Solver. $-$ Include two printouts as exhibits at the end of your report: $1.$ The Excel Solver Sheet showing your model setup and solution. $2.$ The Solver Answer Report generated by Excel. $($You may insert screenshots using PrintScreen$).$