Comet Enterprises assembles hand$-$held vacuum cleaners and desk fans in Memphis, TN$.$ Each vacuum cleaner requires one electric motor, $4$ hours of labor, and $20$ ounces of stainless steel, and brings $$12$ profit. Each fan requires one electric motor, $1$ hour of labor, and $10$ ounces of stainless steel, and brings $$4$ profit. There are $100$ electric motors, $160$ hours of labor, and $1100$ ounces of stainless steel available for this week's production.

$($a$)$ Formulate a linear program to determine Comet's production plan for this week to maximize total profit, that is$,$ how many hand$-$held vacuum cleaners, and how many desk fans should the company produce.

$($b$)$ This linear program has been coded in the optimization$-$and$-$simulationmodels$-3330.$xIsx spreadsheet. Solve the model and explain the solution.