Excel's Solver tool has been used in the spreadsheet below to solve a linear programming problem with a minimization objective function and all $$ constraints.

$\backslash$table$[[$Input Section$],[,,,,],[$Objective Function Coefficients$],[,,x,Y,],[,,5,4,],[,5,,,],[,$Constraints,,,Req'd$],[,$#$1,4,3,60],[,$#$2,2,5,50],[,$#$3,9,8,144],[,,,,],[$Output Section$],[,,,,],[,$Variables,$9\mathrm{.}6,7\mathrm{.}2,],[,$Profit,$48,28\mathrm{.}8,76\mathrm{.}8],[,,,,],[,$Constraint,Usage,Slack,$],[,$#$1,60,1\mathrm{.}35E-11,],[,$#$2,55\mathrm{.}2,-5\mathrm{.}2,],[,$#$3,144,-2\mathrm{.}62E-11,]]$

a$.$ Give the original linear programming problem.

b$.$ Give the complete optimal solution.