Problem 1. [20 points] A small engineering consulting firm has three senior desi

Question

Problem 1. [20 points] A small engineering consulting firm has three senior designers available to work on the firm's four current projects over the next two weeks. Each designer has 80 hours to split among the projects. The following table shows the manager's scoring (0-nil to 100-perfect) for the capability of each designer to contribute to each project, along with his estimate of the hours that each project will require. Project Designer 90 80 10 50 60 70 50 65 70 40 80 8:5 Hours required70 40 80 35 2 The manager wants to assign designers to maximize the average capability score for all work while ensuring the worst-case capability for any particular project is at least 50. Do not worry about scheduling (eg whether designers can work simultaneously or in some order). Formulate a linear program. Clearly define in words what your decision variables represent. In the LP, label each constraint with a keyword for what the constraint corresponds to. You do not need to solve the LP.

Explanation / Answer

Given Problem :

Row Minimisation :

Column Minimisation

Optimization :

If each designer has 80 hrs availeble then there can be minimisation of Designers.

Total time required = 70 + 50 + 85 + 35 = 240

Total Designers = 240 / 80 = 3

Total designers = 3

3 Designers can work & complete the given task.

P1 P2 P3 P4 Designer 1 90 80 25 50 Designer 2 60 70 50 65 Designer 3 70 40 80 85 Designer 4 65 55 60 75 Time 70 50 85 35

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