$3\mathrm{.}5.$ Consider a resource$-$allocation problem having the following data.

$\backslash$table$[[,\backslash$table$[[$Resource Usage per$],[$Unit of Each Activity$]],,,],[$Resource$,1,2,3,4,\backslash$table$[[$Amount of$],[$Resource$],[$Available$]]],[$P$,3,5,-2,4,400],[Q,4,-1,3,2,300],[R,6,3,2,-1,400],[$S$,-2,2,5,3,300],[$Contribution$,$$$11,$$$9,$$$8,$$$9,],[$per unit,,,,,$]]$

Contribution per unit $=$ profit per unit of the activity.

$($a$.)$ Formulate a linear programming model for this problem on a spreadsheet.

b$.$ Make five guesses of your own choosing for the optimal solution. Use the spreadsheet to check each one for feasibility and, if feasible, for the value of the objective function. Which feasible guess has the best objective function value?

C$.$ Use Solver to find an optimal solution.