$4$You are given the following data for a linear programming problem where the objective is to minimize the cost of conducting two nonnegative activities to achieve three benefits that do not fall below their minimum levels.a$)$ Formulate a linear programming model for this problem and use the graphical method to solve the model. $[25]$b$)$ Display the model on an Excel spreadsheet and use the spreadsheet to check the following solutions: $($x$1,$ x$2)=(7,7),(7,8),(8,7),(8,8),(8,9),(9,8)$ and identify which of these solutions are feasible. Which of these feasible solutions has the best value of the objective function? $[25]$ c$)$ Use the Excel Solver to solve this model by the simplex method. $[25]$