1
2
3
Total
/25
/45
/30
/100
Economics 172A Midterm Exam
NAME________________________________
Vincent Crawford
Winter 2008
Your grade from this exam is 35% of your course grade. The exam ends promptly at 9:20, so you
have 80 minutes. You may not use books, notes, calculators or other electronic devices.
(Calculators shouldn’t be needed.) There are three questions, weighted as indicated. Answer them
all. If you cannot give a complete answer, try to explain what you understand about the answer.
Write your name in the space above, now. Write your answers below the questions, on the back of
the page, or on separate sheets. Explain your arguments and show your work. Good luck!
1. (25 points) 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% 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
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 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.
Letting M = number of men’s gloves to produce per week, W = number of women’s gloves
to produce per week, C = number of children’s gloves to produce per week, F = number of full-time
workers to employ, and P = number of part-time workers to employ, formulate a linear
programming model for this problem, and put it into standard form (with only
≤
constraints).
[Choose M, W, C, F, P to maximize