You are asked to solve the following linear programming problem max 5t1 8t2 5t3 + 3t4 + 3t5 4t6

s.t. 2t1 + 3t2 + t3 2t5 t6 = 9

t1 + t2 + 2t3 + 3t6 = 10

2t2 t3 + 3t4 + 4t5 + 2t6 = 5

+ t2 + t5 + 3t6 5

2t1 + 3t3 t4 + 2t5 + t6 8

t1, t2, t3, t4, t5, t6 0.

Additional information about this problem suggests that, if an optimal solution t exists, then t 4 = 3, t 5 = 0, and t 6 = 1. You may use this information to find t if you so want but you need to justify your answer (in particular, you need to show the optimality of your solution t if you find one).