Sand Mandala Carrie meticulously calculated the early and late start and finish times for her latest project and recorded them using different colors of sand on a pristine slab of white marble. She used red for late start and late finish times and green for early start and early finish times. Activity durations and Project their identifiers were written with black sand. She finished her task and had an opportunity to admire her work only briefly before a colleague came by and swept most of it away. Sadly, this was before Carrie could record the numbers on a more permanent medium, so now she turns to you to help. Activity A Predecessor Duration Early Start Early Finish Late Start Late Finish 10 B - 7 11 A 7 D A 15 14 E B 11 19 F B 10 G D,E 24 H F 24 J K G.H,J 28 36 A) What is the early finish time for activity K? B) What is the slack time for activity H? How many tractors and saws should be produced to maximize profit, and how much profit will they make? Table 3.8: Tracksaws, Inc. Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of $30 on each tractor and $30 on each lawn mower, and they sell all they can produce. The time requirements in the machine shop, fabrication, and tractor assembly are given in the table. Machine Shop Tractor Lawn Mower 2 hours 1 hour Hrs. Available 60 hours Formulation: Fabrication 2 hours Assembly 1 hour 3 hours 0 hour 120 hours 45 hours Let x number of tractors produced per period y=number of lawn mowers produced per period MAX 30x + 30y subject to 2x + y 60 2x + 3y 120 X45 The graphical solution is shown below. 70 60 10 50 40 10 Y Z* 30 20 10 0 0 10 20 30 8 50 60 60 70