The Swelte Glove Company manufactures and sells two products. The company makes a profit of $$12$ for each unit of Sproduct $1$ sold and a profit of $$4$ for each unit of product $2.$ The labor$-$hour requirements for the products in each of the three production departments are summarized in the following table.

Labor$-$Hour Requirement

Department

Product $1$

Product $2$

$1$

$2$

$3$

$1$

$1$

$2$

$2$

$3$

$3$

The supervisors of these departments have estimated that the following numbers of labor hours will be available during the next month: $800$ hours in department $1,600$ hours in department $2,$ and $2000$ hours in department $3.$ Formulate a spreadsheet model of this linear programming $($LP$)$ problem and solve it to maximize profits using the Excel Solver.