# # 17. Scott and Associates, Inc., is an accounting firm that has three new clients. Project leaders will be assigned to the three clients. Based on the different backgrounds and experiences of the leaders, the various leader-client assignments differ in terms of projected completion times. The possible assignments and the estimated completion times in days are as follows:                                                       ClientProject Leader                        1         2           3Jackson                                   10       16         32Ellis                                          14       22        40Smith                                       22       24        34 a. How many constraints are there in the linear program (not including the non-negativity constraints)?b. What is the total completion time in days?

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Asked Nov 21, 2019
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# 17. Scott and Associates, Inc., is an accounting firm that has three new clients. Project leaders will be assigned to the three clients. Based on the different backgrounds and experiences of the leaders, the various leader-client assignments differ in terms of projected completion times. The possible assignments and the estimated completion times in days are as follows:
Client
Project Leader                        1         2           3
Jackson                                   10       16         32
Ellis                                          14       22        40
Smith                                       22       24        34
a. How many constraints are there in the linear program (not including the non-negativity constraints)?
b. What is the total completion time in days?

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Step 1

To solve the linear programming problems. first identify the constraints and then use excel to solve it.

Step 2

Assume variables x11, x12, x13, x21, x23, x23, x31, x32 and x33. Such that x11 corresponds to the link between Jackson and client1 and so on.

As, every project leader could have total of atmost 1 client. So, sum of their contribution to all client must be less than or equal to 1.

As every client should have total of exactly 1 project. So, sum of contribution for one client from 3 project leaders must be 1.

So, constraints will be,

Step 3

Hence, in total of 6 constraints are there and th...

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