For each problem you formulated for homework assignment 1, solve by the graphical method demonstrated in class on January 25. Clearly show the boundary of each constraint, shade in the feasible region, draw at least one isoprofit or isocost line, and show an isoprofit/isocost line tangent to the feasible region at the optimal point (or set of optimal points). Show your work in solving the two equations in two unknowns that identify an optimal point.
Note that for each problem, you are only doing part "b" in the book. You already did part "a" for assignment 1. If you are unsure your answers to assignment 1 were correct, official solutions will be posted at http://business.rutgers.edu/eckstein/om-spring-2005.html on February 2 (I cannot post the solutions sooner because other sections are using the same assignment).
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 (remember the hints I gave in class).
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.