a) is the optimal solution sensitive to the exact value of the packaging hours available? At what number of hours capacity would it become relevant? b) How much should BF Company be willing to pay for an additional hour of assembly time? c) What would be the profit effect of increasing assembly capacity to 750 hours? To 980hours? d) What would be the profit effect of increasing the profit margin on modelX by $200 per unit? What would be the effect of a decrease in that amount? XBright Future (BF) Company is producing two different laptops: modelx, modelz. modelx brings $300, model brings $250 profit for BF company. Demands for modelX and modelZ are forecasted to be 200 and 100 during the month. Production processes for either model are assembly, polishing, and packaging. modelx consumes 1.5 hours of assembly time per unit, 0.3 hour of polishing, and 0.2 hour of packaging. Corresponding values per unit of modelZ are 2, 0.5, and 0.4. There are 600 hours of assembly time, 200 hours of polishing, and 150 hours of packaging time available over the next month. The problem's LP model and AMPL output are given (main constraints are named in order c1,c2,...,c5; x1 is used for modelx, x2 is used for modelz): maximize 300x1 + 250x2 subject to X1200 X2 > 100 1.5X1 + 2x2 5 600 0.3x1 + 0.5x2 s 200 0.2x1 + 0.4x2 0 : _varname 1 x1 2 x2 ; _var 266.667 100 _var.rc _var.current _var.up_var. down 300 1e+20 187.5 0 250 400 -1e+20 # $5 - _con.current : _conname_con.body _con.slack _con. dual $5 _con.up _con. down 1 2 3 4 5 c1 c2 c3 c4 c5 266.667 100 600 130 93.3333 66.6667 0 0 70 56.6667 0 - 150 200 0 0 200 100 600 200 150 266.667 150 950 1e+20 1e+20 -1e+20 0 500 130 93.3333