Answer Happy

OPTION 1 WeServe Ltd provides contract engineers to client companies for projects. Four of their customers have requested engineering cover for projects that will begin next week. WeServe Ltd have a pool of six qualified Engineers that can be assigned to these projects. But each engineer has a maximum of 25 hours per week to devote to serving these clients. For a variety of reasons, the profit resulting from assigning engineers to projects varies as shown in the table below (in hundreds of euro per hour). Service Engineer Client Company 2 3 10 6 5 8 7 5 11 10 1 10 5 5 6 10 4 5 12 6 6 10 Management's objective is to determine the assignment of engineers to clients in order to maximise the profit to the company. Solve the problem for the following cases: (a) Assume that each client must receive exactly 35 hours of engineering cover per week. An engineer can have their allocated hours divided across multiple clients and a client can be assigned two or more engineers to cover their requirements. (b) Now assume that an engineer may be assigned to work up to 40 hours per week. However, if an engineer is assigned more than 25 hours per week, they get paid an extra €100 per hour. Each client must still receive exactly 35 hours of engineering cover per week. (c) Now assume that an engineer must receive exactly 25 hours work with a single client per week (i.e. an engineer will not be allocated to two or more clients per week) and at most two engineers will be allocated to a client. The choice of these assignments of engineers to clients is to be made solely on the basis of maximising total profit, not on number of hours required by the client (assume each client will find 25 hours' worth of project work per engineer they are assigned). The following is required in answering this question, for each part: (1) Construct the appropriate cost and requirements table. (2) Explain how the table was constructed. (3) Give the solution to the problem. Note: these problems can be solved using MS Excel Solver. The solution will include the total profit and the assignments of engineers to clients and hours to be worked. (4) Give in words a brief explanation of the solution, and reasons why you think the solution gives a valid answer to the problem. In addition to the above, provide and explain the LP model for part (a) and show how this model had to be amended for the conditions described in part (b) and part (c).