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Question Number 113455 by AbhishekBasnet last updated on 13/Sep/20
Commented by som(math1967) last updated on 13/Sep/20
Numberofonekindxandotherkindyx⩾0,y⩾0150x+75y⩽150050x+75y⩽600Max.profit=Pmax=5x+3yCornerpointsare(0,0),(10,0),(9,2),(0,8)∴Pmaxat(9,2)=5×9+3×2=Rs51
Answered by 1549442205PVT last updated on 13/Sep/20
Supposefirstkindofcakeismadexboxesandsecondkindofcakesismadeyboxes.Fromthehypothesiswehasthesystem:{150x+75y=1500(1)50x+75y=600(2)Substractingtwoequationsweget100x=900⇒x=9.Replacewegety=2.Thentheprofitsobtainequalto9×5+2×3=51(Rs)∙Ifmade10boxesoffirstkindofcakesthenthesecondkindofcakeshasnoboxesbecause10×150=1500grflour,sohasnoflourtomakesecondkindofcakes∙Fromaboveresultweinfera+b⩽11anda⩽9⇒b⩽11−aTheprofitsvalueobtainisM=5a+3b⩽5a+3(11−a)=2a+33⩽2×9+33=51Thus,thebestoptionforcandyproductare9boxesof1typeand2boxesof2type
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