# Operations Management: Optimization and Linear Programming – #29506

Question: Hands-on is a company that features a product line of winter gloves for the entire family— men, women, and children. They want to decide what mix of these three types of gloves to produce.

The Hands-on’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:

(i) Each part-time worker works 20 hours per week, and;

(ii) There must be at least two full-time employees for each part-time employee.

In terms of the manufacturing process, all three types of gloves are made out of the same 100 percent genuine cowhide leather. Hands-on has a long-term contract with a supplier of the leather and receives a 5,000 square-foot shipment of 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 below:

 Glove Material Required (Square Feet) Labor Required (Minutes) Gross Profit (per pair of gloves) Men’s 2 30 $8 Women’s 1.5 45 10 Children’s 1 40 6 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-tiMeand part-time workers to employ while they would like to maximize their net profit—their gross profit from sales minus their labor costs.

Formulate and solve a linear programming model to determine the best mix of gloves and employees to have to maxmize their net profit. Be clear and identify/describe the decision variables, constraints and objective function.