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 5,000-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.

Each full-time employee earns $13 per hour, while each part-time employee earns $10 per hour. 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. They would like to maximize their net profit -their gross profit from sales minus their labor costs.
a. Formulate and solve a linear programming model for this problem on a spreadsheet.
b. Summarize this formulation in algebraic form.

Material Labor Gross Profit (Minutes) (per Pair) Required Required (Square Feet) Glove Men's Women's 30 45 1.5 1 10 40 6. Children's