3.4-17. Comfortable Hands is a company which features a prod- uct 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 per- cent 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. Material Required Labor Required Gross Profit (Minutes) Glove (Square Feet) (per Pair) Men's 30 $8 $10 $6 2 Women's 1.5 45 Children's 1 40 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 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. c (b) Solve this model by the simplex method.
3.4-17. Comfortable Hands is a company which features a prod- uct 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 per- cent 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. Material Required Labor Required Gross Profit (Minutes) Glove (Square Feet) (per Pair) Men's 30 $8 $10 $6 2 Women's 1.5 45 Children's 1 40 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 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. c (b) Solve this model by the simplex method.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Transcribed Image Text:3.4-17. Comfortable Hands is a company which features a prod-
uct 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 per-
cent 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.
Material Required Labor Required Gross Profit
(Minutes)
Glove
(Square Feet)
(per Pair)
Men's
30
$8
$10
$6
2
Women's
Children's
1.5
45
1
40
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 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.
c (b) Solve this model by the simplex method.
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