Comfortable Hands is a company which 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’ 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 can also 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 2 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 feet shipment of the material each week. The material requirements and labor requirements, along with the gross profit per glove sold (not considering labor costs) is given in the following table.
Glove Materials Required (Square feet) Labour Required (Minutes) Gross Profit (Per pair)
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 parttime 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 how many part-time workers to employ. They would like to maximize their net profit—their gross profit from sales minus their labor costs.
a. Formulate a linear programming model for this problem. (12 marks)
b. Solve this model using Excel’s Solver and show the sensitivity report for variables and constraints. (13 marks)
c. Interpret the result of the sensitivity report and offer Comfortable Hands the necessary advice. The interpretation should include at least the following:
Reduce cost, Shadow price, resource usage, constraints binding and non-binding.
