All questions, plz!

(total on this page: 16.5 points) 1. You run an optimization model and you found an optimal solution. The values of the two decision variables \\( X_{1} \\) and \\( X_{2} \\) at the optimal solution are 7 and 0 respectively. What is the reduced cost for \\( X_{1} \\) ? (1.5 point) 2. Given the two constraints: \\( X_{1} \\leq 70 \\) and \\( X_{2} \\leq 50 \\). The constraint for \\( X_{2} \\) can be described as a constraint. (1.5 point) 3- A solution is optimal only if it has a unique solution. ( 1.5 point) a. True b. False 4- What is a balanced constraint? ( 2 points) 5. In a minimal spanning tree model, three conditions must be met, what are they? ( 2 points) 6- In a maximal flow problem, a flow of material in a path is limited by the largest capacity in that path. (1.5 point) a. True b. False 7- A feasible region in a graphical solution is defined by the constraint equations in the problem. (1.5 point) a. True b. False 8- In a minimal spanning tree algorithm, you can choose any node as a starting point to find an optimal solution. (1.5 point) a. True b. False 9- The objective in any shortest-route problem is to maximize the total distance from the origin node to the destination node. ( 1.5 point) a. True b. False 10- Given the following objective function: Max \\( 4 X+3 Y \\). If this problem has only two constraints, which are \\( X \\geq \\) 10 and \\( Y \\geq 5 \\), what can you say about output of this model? ( 2 points)