For each problem listed below, first write out an algebraic linear program as we did at the end of the first class. Use the "standard" format, starting with clear definitions of the decision variables as numbers. For example, write "x1 = number of regular bags produced," not "x1 = regular". Give this kind of definition for every variable. Once you have defined the variables, write the problem out in the form:
| { | Minimize
or Maximize |
} | Objective Function |
| Subject To | Constraint 1 | ||
| Constraint 2 | |||
| etc. |
Customarily, the constraints involving more than one decision variable are listed first, followed by the simpler constraints like "x1 > 0". (Note: these conventions are not critically important, but make grading easier.)
Second, for each problem listed below, create an Excel spreadsheet model of the problem and find an optimal solution with Solver. Hand in the standard printouts.
For each
problem, ignore parts "a" and "b" in the book. Just follow the above
instructions instead -- you do not have to solve the problem graphically for
this assignment.
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). Don't forget the
constraint that they must produce at least twice as many chairs as they do
desks, which will look a little different from the constraints done so far 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? Note: you will probably want to use "min" instead of "max" in your objective function, and your constraints will have ">" instead of "<".