1. Pawtucket University is planning to buy new copier machines for its library. Three members
of its Operations Research Department are analyzing what to buy. They are considering two
different models: Model A, a high-speed copier, and Model B, a lower-speed but less expensive
copier. Model A can handle 20,000 copies a day, and costs $6,000. Model B can handle 10,000
copies a day, but costs only $4,000. They would like to have at least six copiers so that they can
spread them throughout the library. They also would like to have at least one high-speed copier.
Finally, the copiers need to be able to handle a capacity of at least 75,000 copies per day. The
objective is to determine the mix of these two copiers which will handle all these requirements at
minimum cost.
(a) Formulate an IP model for this problem.
(b) Use a graphical approach to solve this model.
(c) Solve the model.
2. Use the BIP branch-and-bound algorithm to solve the following problem interactively.
Minimize Z = 5x1 + 6x2 + 7x3 + 8x4 + 9x5
Subject to
3x1 - x2 + x3 + x4 - 2x5 ≥ 2
x1 + 3x2 - x3 - 2x4 + x5 ≥ 0
-x1 - x2 + 3x3 + x4 + x5 ≥ 1
and
xj is binary, for j = 1, 2, 3, 4, 5.
3. Use the MIP branch-and-bound algorithm to solve the following MIP problem interactively.
Minimize Z = 5x1 + x2 + x3 + 2x4 + 3x5,
Subject to
x2 - 5x3 + x4 + 2x5 ≥ -2
5x1 - x2 _ x4 + x5 ≥ 7
x1 + x2 + 6x3 + x4 ≥ 4
and
xj ≥ 0, for j = 1, 2, 3, 4, 5.
xj is integer, for j = 1, 2, 3.