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Back Savers Production Problem

Back Savers Production Problem

Back Savers is a company that produces backpacks primarily for students. They are considering offering some combination of two different models$-$the Collegiate and the Mini.

Both are made out of the same rip$-$resistant nylon fabric. Back Savers has a long$-$term contract with a supplier of the nylon and receives a $5,000-$square$-$foot shipment of the material each week.

Each Collegiate requires $3$ square feet while each Mini requires $2$ square feet. The sales forecasts indicate that at most $1,000$ Collegiates and $1,200$ Minis can be sold per week.

Each Collegiate requires $45$ minutes of labor to produce and generates a unit profit of $$32.$ Each Mini requires $40$ minutes of labor and generates a unit profit of $$24.$

Back Savers has $35$ laborers that each provides $40$ hours of labor per week. Management wishes to know what quantity of each type of backpack to produce per week in order to maximize the total profit.

a$.$ Formulate and solve a linear programming model for this problem on a spreadsheet.

b$.$ Formulate this same model algebraicall

Exlpain all your answers with detail especially the excel part