1. LINDO output is given for the following linear programming problem. MIN 12 X1 + 10 X2+ 9 X3 SUBJECT TO 2) 5 X1 + 8 X2 + 5 X3 >=60 3) 8 X1 + 10 X2 + 5 X3 >=80 END LP OPTIMUM FOUND AT STEP 1 OBJECTIVE FUNCTION VALUE 1) 80,000000 VARIABLE VALUE REDUCED COST .090000 4.000000 X2 8.000000 .000000 X3 1090000 4.000000 ROW SLACK OR SURPLUS DUAL PRICE 2) 4.000000 .000000 .090000 -1:000000 NO. ITERATIONS=1 RANGES IN WHICH THE BASIS IS UNCHANGED VARIABLE CURRENT OBJ. COFFFICIENT RANGES ALLOWABLE COEFFICIENT INCREASE 12.000000 ALLOWABLE XI INFINITY X2 10.000000 5.000000 DECREASE INFINITY 4.090000 X3 9.000000 10.009000 RIGHTHAND SIDE RANGES 4.0900902. An airline needs mechanics for its romance departments for each day of the week as follows: [7 points] Time # mechanics required Monday 24 Tuesday 35 Wednesday 28 Thursday 18 Friday 10 Saturday 16 Sunday 18 Each mechanic works for 5-day in a row. Just Formulate this problem with the objective function to minimize the total maintenance work force.3. An airline employee is trying to assion .plential weekly routes ( WR). The table below presents the net weekly profit (in 000s ) coming each crew to caen weekly route. This net profits are different because the home base care different Formulate an LP model sry that the net profit is maximized by showing which should be assigned to which weekly route [4 points] Weekly routings WRI WR2 WR3 Crew A 15 20 18 Crew B 20 22 26 Crew C 25 26 27cial airline has regular daily fights in both directions between Atlanta on (BOS). If a crew is based s me city and arrives in the other, then it its base city on a later flight (wahmay be on the following day). In the wishes of the crew the companywishes to choose the return flight so as in immunize the time spent from the respective co's Pick is base cities. There must be at least 15 minutes interval for new between arriving and departing flights. The crew-base base for this airline is Atlan(AILL Given the flight schedules. develop a linear programming model to pair thefights in an effort to minimize the total time the crew stays away from the base. [ DO NOT SOLVE 6 points] Flight NO. Departs ATL Arrives at BOS 1 08:00 10:00 3 15:00 17:00 15 19:00 21:00 Flight NO. Departs BOS Amives at A TI 10:00 12:00 14:00 16:00 17:00 19:0035167m UTO CURRENT ALLOWABLE ALLOWABLE ROW RHS INCREASE DECREASE 60.000000 4.000000 INFINITY 80.000000 INFINITY 5.000000 Answer the following questions in the spaces provided - show your work a. What is the solution to the problem? [ I point] Mos COW b. Which constraints are binding and why? [ 1 point] c. By how much the values of x1 and x3 in the obj. fune should go up or down so that their solution values become non-zero? [ 1 point] d. What does the dual price for constraint 2 mean? [1 point] point] What would happen if the cost of to drummed to 10 and the cost of x2 increased to 127