$<=$ i $<$ j $<=9.$ We wish to develop a linear programming model to determine the minimal spanning

tree for this network.

$($a$)$ For the LP for the minimal spanning tree problem, write the constraint for point of interest $4.$

$($b$)$ For the LP for the minimal spanning tree problem, write the constraint for point of interest $7.$

$($c$)$ Apply Prim$$s algorithm $($i$.$e$.,$ solve by hand$)$ to determine which routes should be used by the

park$$s shuttles. You may highlight or otherwise indicate the selected routes on the diagram

itself. Which connections are used, and what is the total time?