2019-03-04T12:56:37+00:00

Linear Programming Examples

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Linear Programming Examples

Solve the linear programming models using either lp_solve (recommended, see linear programming tutorial) or excel solver (Google for details).
Include mathematical models.

1. A company has 4 projects to be assigned among 3 employees. Find the assignment that minimizes the total time spent by the employees:

Peter Mary Joan
Project 1 2 weeks 3 week 4 weeks
Project 2 3 weeks 2.5 weeks 5 weeks
Project 3 4 weeks 3.5 weeks 3 weeks
Project 4 6 weeks 3 weeks 3.5 weeks

2. A cab company has four cabs. Three customers are requesting the service. Assign the cabs to the customers such that revenue is maximized.

Customer 1 Customer 2 Customer 3
Taxi 1 $300 $250 $280
Taxi 2 $195 $228 $318
Taxi 3 $198 $193 $308
Taxi 4 $150 $325 $240

3. ACME construction build homes in Albany, GA. The company has $300,000 dollars to be invested next month. Table below show potential construction sites, cost of buildings and Expected profits:

Location Building cost Expected Profit
Clifton 60,000 5,000
Auburn 50,000 6,000
Adams 82,000 10,000
Amberly 103,000 12,000
Norwood 50,000 8,000
Covington 41,000 3,000
Roselawn 80,000 9,000
Eden 69,000 10,000

a. Find the set of projects that maximizes profits.

4. (From a previous final) A company has 3 million dollars for new projects in a manufacturing facility. Move over, there is limited space (1500 ft2) and only 15 employees to be assigned to the projects. Below is a summary of ten projects recommended by the plant manager:
Project Projected Revenue [$M] Required Investment Required Employees Required Space
1 0.65 0.5 7 248
2 0.48 0.4 3 215
3 0.84 0.7 2 261
4 0.48 0.7 7 272
5 0.55 0.5 6 342
6 0.66 0.4 8 235
7 0.44 0.6 3 298
8 0.66 0.7 5 444
9 0.84 0.7 2 439
10 0.36 0.3 5 366

Select the set of projects that maximizes company`s revenue.


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