Please answer ALL with explanation and correct answer.

Refer to the following figure. The shaded region is the feasible solution to a linear program whose objective is to maximize ax 1+bx2. What is the optimal solution? What is the optimal solution to the following optimization problem maxs.t.x1+3x2x1+2x24x1+x23x10x20 What is the optimal solution to the following optimization problem? maxs.t.5x1+x2+11x35x14x2+6x373x1+6x2+7x3116x1+5x2x352x10x20x30x1,x2,x3areintegers (A) (0,0,0) (B) (0,0,1) (C) (3,3,0) (D) None of above (E) (1,2,0) Consider the transportation problem with 4 suppliers and 3 customers. The unit transportation costs between suppliers and customers are given in the following table. Also, the table includes the total inventory levels of the suppliers and the order quantities of the customers. Calculate the total transportation cost for the optimal distribution plan that satisfies the supply and demand constraints. Do not include the dollar (\$) symbol in your answer. Consider the binary variables x1,x2,x3,x4, and x5 where xi is defined as 1 if object i is selected and 0 otherwise. Which of the following inequality models the requirement: Both x2 and x3 are selected if x5 is selected. Otherwise, at least one of x2 and x3 is selected. (A) x2+x3>=x5 (B) 2+3>=1+5 (C) x2+x3>=2 (D) x2+x3=x5 (B) 2+3>=1+5 (C) x2+x3>=2 (D) x2+x3