Linear programming is a powerful tool that can be used by university administrations to make optimal decisions regarding resource allocation and production planning. In this problem, we consider a linear programming problem faced by the University of Ghana Business School $($UGBS$)$ administration. The UGBS offers four main products: undergraduate degrees $($x$1),$ graduate degrees $($x$2),$ online courses $($x$3),$ and professional development programs $($x$4).$ Each product has specific requirements in terms of resources, such as faculty, staff, classroom space, technology, and funding. To maximize revenue while managing resources effectively, the UGBS must find the right balance of product offerings. Unit Revenue contributions per each product offering are $100,000,250,000,5,000$ and $10,000$ for undergraduate degrees, graduate degrees, online courses, and professional development programs $,$ respectively. The UGBS has six resource constraints, namely; faculty, staff, classroom space, technology, funding for scholarships and funding for research. It has the following amount of each of these resources available. Faculty: $100$ professors, Staff: $50$ administrative staff, Classroom space: $100$ classrooms, Technology: $500$ computers, Funding for scholarships: GHc$1$ million, Funding for research: GHc$5$ million The UGBSs production requirements for each product are: Undergraduate degrees: $4$ faculty members, $2$ administrative staff, $2$ classrooms, $50$ computers, GHc$20,000$ scholarship funding, and GHc$100,000$ research funding Graduate degrees: $6$ faculty members, $4$ administrative staff, $3$ classrooms, $75$ computers, GHc$50,000$ scholarship funding, and GHc$250,000$ research funding Online courses: $1$ faculty member, $1$ administrative staff, $1$ classroom, $10$ computers, GHc$5,000$ scholarship funding, and GHc$10,000$ research funding Professional development programs: $2$ faculty members, $1$ administrative staff,$1$ classroom, $7$ computers.All answers with decimals must be to $2$ decimal placesModel the entire problem with Microsoft Excel Solver and answer the following question. a$.$State the Non$-$negativity constraint. Blank $1.$ Fill in the blank, read surrounding text. $,$ Blank $2.$ Fill in the blank, read surrounding text. $,$ Blank $3.$ Fill in the blank, read surrounding text. $,$ Blank $4.$ Fill in the blank, read surrounding text. $.$ b$.$ What is the objective function value? Blank $5.$ Fill in the blank, read surrounding text. c$.$ What are the the two optimal solution values? Blank $6.$ Fill in the blank, read surrounding text. $,$ Blank $7.$ Fill in the blank, read surrounding text. d$.$ What are the reduced cost values? Blank $8.$ Fill in the blank, read surrounding text. $,$ Blank $9.$ Fill in the blank, read surrounding text. e$.$ What is the maximum shadow price value. Blank $10.$ Fill in the blank, read surrounding text. f$.$ How many binding constraints are in the solution? Blank $11.$ Fill in the blank, read surrounding text. g$.$ Compute the minimum number of faculty the school is allowed to provide. Blank $12.$ Fill in the blank, read surrounding text. h$.$ Compute the maximum research funding the school can receive. Blank $13.$ Fill in the blank, read surrounding text. i$.$ How many non$-$binding constraints is shown in the sensitivity report? Blank $14.$ Fill in the blank, read surrounding text. j$.$ Which of the product contributes the highest revenue?