New Exercise Bank Content Qu$.06-23$

Comfortable Hands is a company that features a product line of winter gloves for the entire family$-$men, women, and children. They are trying to decide what mix of these three types of gloves to produce. Comfortable Hands's manufacturing labor force is unionized. Each full$-$time employee works a $40-$hour week. In addition, by union contract, the number of full$-$time employees can never drop below $20.$ Nonunion, part$-$time workers also can be hired with the following union$-$imposed restrictions: $(1)$ each part$-$time worker works $20$ hours per week and $(2)$ there must be at least two full$-$time employees for each part$-$time employee. All three types of gloves are made out of the same $100$ percent genuine cowhide leather. Comfortable Hands has a long$-$term contract with a supplier of the leather and receives a $5,400-$square$-$foot shipment of the material each week. The material requirements and labor requirements, along with the gross profit per glove sold $($not considering labor costs$),$ are given in the following table.

$\backslash$table$[[$Gross Profit $($per glove$),$Men's,Women's $$20,$Children $$12],[,$Resource Usage per Unit of Activity$],[,$Men's,Women's,Children's$],[$Material $($square feet$),2,1\mathrm{.}5,1],[$Labor $($minutes$),30,45,40]]$

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

Each full$-$time employee earns $$26$ per hour, while each part$-$time employee earns $$20$ per hour.

a$.$ Management wishes to know what mix of each of the three types of gloves to produce per week, as well as how many full$-$time and part$-$time workers to employ.

Note: Leave no cells blank. Enter $"$O$"$ wherever required.

$\backslash$table$[[,$Men's,Women's,Children's$],[$Production $($per week$),,,],[$Employees$,$Full Time,Part Time,$]]$

b$.$ Determine the net profit.

Net profit