ESI 6314
Sample Exam #1 Solutions
1.
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 fulltime
employee works a 40hour week. In addition, by union contract, the number of fulltime
employees can never drop below 20. Nonunion, parttime workers can also be hired with
the following unionimposed restrictions: (1) each parttime worker works 20 hours per
week, and (2) there must be at least 2 fulltime employees for each parttime employee.
All three types of gloves are made out of the same 100% genuine cowhide leather.
Comfortable Hands has a longterm 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
Material Required
(square feet)
Labor Required
(minutes)
Gross Profit
(per pair)
Men’s
2
30
$8
Women’s
1.5
45
$10
Children’s
1
40
$6
Each fulltime 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 fulltime and how many parttime workers to
employ. They would like to maximize their
net profit
— their gross profit from sales
minus their labor costs.
Formulate a linear programming model for this problem.
Decision variables: M = # of pairs of men’s gloves produced
W = # of pairs of women’s gloves produced
C = # of pairs of children’s gloves produced
F = # of fulltime employees
P = # of parttime employees
Maximize Z = 8M + 10W + 6C – (40*13)F – (20*10)P
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 Fall '09
 VLADIMIRLBOGINSKI
 Optimization, ice cream, optimal solution, hands, alternative optimal solution

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