The Livewright Medical Supplies Company has a total of 12 salespeople it wants to assign to
three regions – the South, the East, and the Midwest. A salesperson in the South earns $600 in
profit per month of the company, a salesperson in the East earns $540, and a salesperson in the
Midwest earns $375. The southern region can have a maximum assignment of 5 salespeople.
The company has a total of $750 per day available for expenses for all 12 salespeople. A
salesperson in the South has average expenses of $80 per day, a salesperson in the East has
average expenses of $70 per day, and a salesperson in the Midwest has average daily expenses
of $50. The company wants to determine the number of salespeople to assign to each region to
Formulate an integer programming model for this problem
Solve this model by using the computer.
Solve the following mixed integer linear programming model by using the computer:
MaximizeZ=5x1 +6x2 +4x3
5x1 +3x2 +6x3 ≤20
x1+3x2 ≤12x1, x3 ≥ 0x2 ≥ 0 and integer
3. The Texas Consolidated Electronics Company is contemplating a research and development
program encompassing eight research projects. The company is constrained from embarking on
all projects by the number of available management scientists (40) and the budget available for
R&D projects ($300,000). Further, if project 2 is selected, project 5 must also be selected (but
not vice versa). Following are the resource requirements and the estimated profit for each
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Formulate the integer programming model for this problem and solve it using the computer.
4. During the war with Iraq in 1991, the Terraco Motor Company produced a lightweight, all-
terrain vehicle code-named “J99-Terra” for the military. The company is now planning to sell
the Terra to the public. It has five plants that manufacture the vehicle and four regional
distribution centers. The company is unsure of public demand for the Terra, so it is considering
reducing its fixed operating costs by closing one or more plants, even though it would incur an
increase in transportation costs. The relevant costs for the problem are provided in the
following table. The transportation costs are per thousand vehicles shipped; for example, the
cost of shipping 1,000 vehicles from plant 1 to warehouse C is $32,000.
Transportation Costs ($1000s)
Formulate and solve an integer programming model for this problem to assist the company in
determining which plants should remain open and which should be closed and the number of
vehicles that should be shipped from each plan to each warehouse to minimize total cost.