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Advanced MathQ&A Library# 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?Question

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?

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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