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Exhibit 61
the Following Questions Pertain to the Problem,formulation,and Spreadsheet Implementation

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Exhibit 6.1
The following questions pertain to the problem,formulation,and spreadsheet implementation below.
A research director must pick a subset of research projects to fund over the next five years.He has five candidate projects,not all of which cover the entire five-year period.Although the director has limited funds in each of the next five years,he can carry over unspent research funds into the next year.Additionally,up to $30K can be carried out of the five-year planning period.The following table summarizes the projects and budget available to the research director.
Project Funds Required in $000s)Benefit
 Project 12345 in $000s)1$70$40$30$15$15$1602$82$35$20$20$10$1903$55$10$10$5$1254$69$17$15$12$8$1395$75$20$25$30$45$174\begin{array}{ccccccc}\text { Project } & 1 & 2 & 3 & 4 & 5 & \text { in } \$ 000 s) \\\hline 1 & \$ 70 & \$ 40 & \$ 30 & \$ 15 & \$ 15 & \$ 160 \\2 & \$ 82 & \$ 35 & \$ 20 & \$ 20 & \$ 10 & \$ 190 \\3 & \$ 55 & \$ 10 & \$ 10 & \$ 5 & & \$ 125 \\4 & \$ 69 & \$ 17 & \$ 15 & \$ 12 & \$ 8 & \$ 139 \\5 & \$ 75 & \$ 20 & \$ 25 & \$ 30 & \$ 45 & \$ 174 \\\hline\end{array}
Budget $225K $60K $60K $50K $50K The following is the ILP formulation and a spreadsheet model for the problem.
 Exhibit 6.1 The following questions pertain to the problem,formulation,and spreadsheet implementation below. A research director must pick a subset of research projects to fund over the next five years.He has five candidate projects,not all of which cover the entire five-year period.Although the director has limited funds in each of the next five years,he can carry over unspent research funds into the next year.Additionally,up to $30K can be carried out of the five-year planning period.The following table summarizes the projects and budget available to the research director. Project Funds Required in $000s)Benefit   \begin{array}{ccccccc} \text { Project } & 1 & 2 & 3 & 4 & 5 & \text { in } \$ 000 s) \\ \hline 1 & \$ 70 & \$ 40 & \$ 30 & \$ 15 & \$ 15 & \$ 160 \\ 2 & \$ 82 & \$ 35 & \$ 20 & \$ 20 & \$ 10 & \$ 190 \\ 3 & \$ 55 & \$ 10 & \$ 10 & \$ 5 & & \$ 125 \\ 4 & \$ 69 & \$ 17 & \$ 15 & \$ 12 & \$ 8 & \$ 139 \\ 5 & \$ 75 & \$ 20 & \$ 25 & \$ 30 & \$ 45 & \$ 174 \\ \hline \end{array}   Budget $225K $60K $60K $50K $50K The following is the ILP formulation and a spreadsheet model for the problem.      -Refer to Exhibit 6.1.What values would you enter in the Analytic Solver Platform task pane for the above Excel spreadsheet? Objective Cell: Variables Cells: Constraints Cells:
 Exhibit 6.1 The following questions pertain to the problem,formulation,and spreadsheet implementation below. A research director must pick a subset of research projects to fund over the next five years.He has five candidate projects,not all of which cover the entire five-year period.Although the director has limited funds in each of the next five years,he can carry over unspent research funds into the next year.Additionally,up to $30K can be carried out of the five-year planning period.The following table summarizes the projects and budget available to the research director. Project Funds Required in $000s)Benefit   \begin{array}{ccccccc} \text { Project } & 1 & 2 & 3 & 4 & 5 & \text { in } \$ 000 s) \\ \hline 1 & \$ 70 & \$ 40 & \$ 30 & \$ 15 & \$ 15 & \$ 160 \\ 2 & \$ 82 & \$ 35 & \$ 20 & \$ 20 & \$ 10 & \$ 190 \\ 3 & \$ 55 & \$ 10 & \$ 10 & \$ 5 & & \$ 125 \\ 4 & \$ 69 & \$ 17 & \$ 15 & \$ 12 & \$ 8 & \$ 139 \\ 5 & \$ 75 & \$ 20 & \$ 25 & \$ 30 & \$ 45 & \$ 174 \\ \hline \end{array}   Budget $225K $60K $60K $50K $50K The following is the ILP formulation and a spreadsheet model for the problem.      -Refer to Exhibit 6.1.What values would you enter in the Analytic Solver Platform task pane for the above Excel spreadsheet? Objective Cell: Variables Cells: Constraints Cells:
-Refer to Exhibit 6.1.What values would you enter in the Analytic Solver Platform task pane for the above Excel spreadsheet?
Objective Cell: Variables Cells: Constraints Cells:


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