Question $5.(21$ points$)$

ABC Strategy Solutions is a leading strategy consulting firm renowned for its dynamic team of consultants. They offer services across multiple areas, and their team consists of professionals at various experience levels: trainee, associate, manager, and partner. The available working hours per month for each role are as follows: $\backslash (\backslash$mathbf$\{100\}\backslash )$ hours for trainees, $\backslash (\backslash$mathbf$\{150\}\backslash )$ hours for associates, $\backslash (\backslash$mathbf$\{200\}\backslash )$ hours for managers, and $\backslash (\backslash$mathbf$\{250\}\backslash )$ hours for partners.

ABC Strategy Solutions handles six types of projects: P$1,$ P$2,$ P$3,$ P$4,$ P$5,$ and P$6.$

The time $($in hours$)$ it takes for each experience level to complete each type of project, as well as the available hours for each experience level, the minimum number of projects that must be completed per month, and the profit per project type are given in the table on this worksheet.

You are asked to determine the optimal number of projects assigned to each expertise level that maximizes the monthly total profit. You will formulate a linear programming model to determine the optimal solution using Excel Solver.

NOTE: SHOW ALL YOUR WORK. USE $4$ DECIMAL PLACES IN YOUR CALCULATIONS.

NOTE: YOU SHOULD PROVIDE AND EXPLAIN ALL STEPS ON YOUR WORKSHEET.

a$)(3$ points$)$ What are the decision variables? How many decision variables are there? Clearly explain the decision variables in English and provide the mathematical notation used in the algebraic formulation of the decision problem.

b$)(2$ points$)$ What is the objective function? Clearly explain the objective function in English and provide the mathematical formulation.

c$)(6$ points$)$ What are the constraints of the problem? Clearly explain each constraint in English and provide the mathematical formulation.

d$)(1$ point$)$ Are there any sign or type restrictions in your formulation? Why or why not? Clearly explain the sign and type restrictions $($if any$).$

e$)(8$ points$)$ Prepare a spreadsheet model and determine the optimal assignment of expertise level hours as well as the optimal objective function value using Excel Solver. Save the Solver parameters windown in your Excel file. What is the optimal solution to this problem? Make sure you save the optimal solution on your spreadsheet.

f$)(1$ point$)$ Which labor hour constraints are binding? Which labour hour constraints are nonbinding $($not binding$)?$ Explain clearly how you determine the binding and nonbinding constraints.

NOTE: MAKE SURE YOU CLEARLY LABEL AND HIGHLIGHT YOUR ANSWERS TO EACH QUESTION.

NOTE: MAKE SURE THE SOLVER PARAMETER WINDOW SAVED ON YOUR WORKSHEET INCLUDES ALL THE INFORMATION FOR PART e$.$