Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver.

The university administration would like to add some additional parking locations. To make everyone happy, they would like each building to be within a $5$ minute walk of at least one set of new parking spaces $($the spaces will be added in blocks of $10$ parking spaces$).$ The university is considering six locations for the new parking spaces, but would like to minimize the overall cost of the project. In addition to the walking time requirement, the university would like to add at least $40$ new parking spaces $($at least $4$ blocks of $10).$ To help with the decision, the management science department formulated the following linear programming model:

Min $400$x$1+375$x$2+425$x$3+350$x$4+410$x$5+500$x$6$

s$.$t$.$ x$1+$ x$2+$ x$5+$ x$61\{$Residence Hall A constraint$\}$

x$1+$ x$2+$ x$31\{$Residence Hall B constraint$\}$

x$4+$ x$5+$ x$61\{$Science building constraint$\}$

x$1+$ x$4+$ x$51\{$Music building constraint$\}$

x$2+$ x$3+$ x$41\{$Math building constraint$\}$

x$3+$ x$4+$ x$51\{$Business building constraint$\}$

x$2+$ x$5+$ x$61\{$Auditorium constraint$\}$

x$1+$ x$4+$ x$61\{$Arena constraint$\}$

x$1+$ x$2+$ x$3+$ x$4+$ x$5+$ x$64\{$Total locations constraint$\}$

xj$=\{1,$if$$location$$j$$is$$selected$0,$otherwisexj$=1,$if$$location$$j$$is$$selected$0,$otherwise

Set up the problem in Excel and find the optimal solution. Which locations are selected?

Multiple Choice

Locations $1,2,3,$ and $5$

Locations $1,2,4,$ and $5$

Locations $1,3,4,$ and $5$

Locations $1,3,$ and $5$

Locations $2,3,4,$ and $5$