A set of jobs $U, V, W, X, Y, Z$ arrive at time $t = 0$ to a production line consisting of two workstations in series. Each job must be processed by both workstations in sequence (i.e., the first followed by the second). The process times (in minutes) for each job on each workstation in the production line are given below.

The sequence in which the jobs must be processed by the production line if the total makespan of production is to be minimized is

A company orders gears in conditions identical to those considered in the economic order quantity (EOQ) model in inventory control. The annual demand is 8000 gears, the cost per order is 300 rupees, and the holding cost is 12 rupees per month per gear. The company uses an order size that is 25% more than the optimal order quantity determined by the EOQ model. The percentage change in the total cost of ordering and holding inventory from that associated with the optimal order quantity is

At the current basic feasible solution (bfs) $v_0 (v_0 \in \mathbb{R}^5)$, the simplex method yields the following form of a linear programming problem in standard form:

minimize $z = -x_1 - 2x_2$

s.t.

$x_3 = 2 + 2x_1 - x_2$

$x_4 = 7 + x_1 - 2x_2$

$x_5 = 3 - x_1$

$x_1, x_2, x_3, x_4, x_5 \geq 0$

Here the objective function is written as a function of the non-basic variables. If the simplex method moves to the adjacent bfs $v_1 (v_1 \in \mathbb{R}^5)$ that best improves the objective function, which of the following represents the objective function at $v_1$, assuming that the objective function is written in the same manner as above?