Operations Management (33:623:386)
Spring 2007
Assignment 2
Wednesday, January 31
For each problem you formulated for homework assignment 1, solve by the
graphical method demonstrated in class. Clearly show the boundary of each
constraint, shade in the feasible region, draw at least one isoprofit or isocost
line, and show the isoprofit/isocost line at the optimal point (or set of
optimal points). Show your work in a hand drawing to scale (on plaid or
graph paper) or as an Excel drawing. Write the values at the points where
each constraint boundary intersects with the horizontal and vertical axes.
Note that for each problem, you are only doing part "b" in the book. You
already did part "a" for assignment 1.
The three questions are repeated below for your convenience, along with
some notes.
Q1. (30 points) Problem 9 on page 23 of the course pack (Bloomington
Brewery).
Q2. (35 points) Problem 2 on page 20 of the course pack (FurnCo desks and
chairs).
Note: be careful graphing the constraint that they must produce at least twice
as many chairs as they do desks. This constraint intersects both axes at 0.
Q3. (35 points) Your firm has a machine that takes large sheets of
cardboard and makes them into boxes used by your shipping department.
The machine is set up to cut the sheets using two possible patterns. When
you use pattern 1, each cardboard sheet becomes 4 small boxes, 2 medium
boxes, and 2 large boxes. When you use pattern 2, each cardboard sheet
becomes 2 small boxes, 3 medium boxes, and 4 large boxes. This week, the
shipping department needs at least 80 small boxes, at least 60 medium
boxes, and at least 30 large boxes. How can you supply their needs, and use
the minimum possible number of cardboard sheets?
Notes: since this is a "min" instead of a "max" problem, you identify the
optimal solution by trying to move isocost lines inward, rather than isoprofit
lines outward. Be careful graphing the constraints (many of which have a
">" instead of "<" form), and note that the feasible region may be infinitely
large and look very different from the example we did in class.