May 25, 2006
Julie Lamberth, Operations Manager for the Mebane, NC, unit of the giant German glove manufacturer, Handschuh
GmbH, is trying to determine her optimal weekly production schedule.
The factory in Mebane has the capability to
produce men’s, women’s, and children’s gloves, all of which are made from the same type of top-grain leather.
factory has a long-term supply contract which guarantees delivery of up to 5000 square feet of leather each week.
Julie has access to full-time unionized workers who put in 40-hour weeks and are paid $18 per hour.
In addition, she
can hire part-time, nonunion workers, who put in 20-hour weeks and are paid $10 per hour.
with the Amalgamated Leather Workers of America (ALWA) specifies that Julie must employ at least 30 full-time
employees at all times and that she must hire at least two full-time employees for each part-time, nonunion employee.
The German corporate office has told Julie to produce at least 3000 pairs of gloves per week, in any mixture of men’s,
women’s, and children’s.
The table below gives various per/pair information about glove production.
profit figure includes all costs,
Formulate a linear program (ignoring obvious integrality issues!) to help Julie determine how many workers to
hire and how many gloves to produce if she wishes to maximize her profit.
Be sure to define all decision
variables (including units) and to identify the sources of the constraints.
If you cannot figure out the decision variables, I’ll sell them to you for 4 points.
The remaining questions present changes to the original scenario.
For each of them, explain how to change your LP
to take the new information into account.
You don’t have to rewrite the entire formulation.
Just indicate the changes.
Questions (B) through (D) are to be answered independently of each other.
( 4) B.
At least 15% of the weekly output is to be children’s gloves.
( 3) C.
No more than 90% of the total labor wages can be spent on full-time workers
( 6) D.
A new leather supplier has appeared on the market and is willing to sell Julie up to 2000 square feet of leather per
week, at a price that is $1.50 more per square foot than the price charged by Julie’s current supplier.
Rodriguez Mexican Foods blends tomatoes, onions, jalapeno peppers, and spices to produce its two brands of salsa: Hot
For the coming season, Rodriguez estimates that it will be able to sell up to 2500 cases of Hot & Fiery salsa and