1) The Reynolds Interpretation Company has accepted a form to set-up a soak disinfection plant; superintendents at Reynolds possess attested the aftercited works to relieve them delay the interpretation of the alien restrain set-uping. In specification to identifying the works needed for this contrivance, they thinkd the prolongation and frequented requires associated delay completing each work at its "Normal" summit (the prolongation delay the narrowness frequented requires) and the prolongation and frequented requires associated delay the "Crash" summit (that is, if the work is maximally sheltered). The superintendents pretend that the final compression requires are fixed (for copy, the final compression require for work B would be ($26,000 - $14,000)/(6 - 4 weeks) = $6000/wk).
Task Description Predecessor Duration(wks) Cost($) Duration(wks) Cost($
A Procure materials Start 3 5,000 2 10,000
B Prepare site Start 6 14,000 4 26,000
C Dpt approval Start 2 2,500 1 5,000
D Prebabricate bldg. A 5 10,000 3 18,000
E Obtain city approvals C 2 8,000 2 8,000
F Install Lines A 7 11,000 5 17,500
G Erect bldg. B,D,E 4 10,000 2 24,000
Totals 61,000 108,000
If all works are effected at their “normal” spells as implied in the board over, the contrivance is thinkd to require Reynolds a entirety of $61,000 in frequented requires and conclusion in an expected contrivance makespan of 12 weeks. However, superintendents at Reynolds nonproduction to inquire the spell-require trade-offs associated delay compressing the contrivance and possess after to you for relieveance.
Specifically, Reynolds' superintendents possess asked you to do the aftercited. Starting delay all works effected at their ordinary prolongation (such that the contrivance makespan is 12 weeks), weaken the makespan of the contrivance by one week at a spell. For each harping (e.g., 11 weeks, 10 weeks, etc), experience the work(s) that should be sheltered to minimize the final growth in frequented requires at each harping. Continue compressing the contrivance until at smallest one hazardous course exists delay all works set at their jar spells (that is, no exalt contrivance compression is feasible). Construct a graph showing the entirety frequented require (on the Y axis) versus the contrivance makespan (on the X axis). Clearly betray the narrowness feasible contrivance makespan.
2) The superintendents at Reynolds Interpretation Company now substantiate that their calculations in whole #1 do not apprehend aloft/infrequented requires that they think at $5100/week (this require apprehends the rental fee for shelter quibble, an aloft interpretation crane needed for the prolongation of this contrivance, and your services as superintendent of this interpretation contrivance). They also possess signed a form that calls for a forfeiture require of $3200 per week for each week that the makespan exceeds ten weeks. Given these requires, formulate and unfold a rectirectilinear programming type that experiences the baseline register that minimizes the entirety requires of this contrivance (where entirety requires are the sum of frequented, indirect/overhead, and forfeiture requires).