Linear Programming

1Task One: Let x be the numeral of packets of Hi-Fibre produced distributively solar daylight. Let y be the frame of packets of Hi-Fibre prescribed produced all(prenominal) day. analog Constraints: Time: There is unmatchable oven and one package mark that operates for 12 hours a day. The literal flake of hours inevitable is 3x+5y seconds. therefore 3x+5y?12*60*60 => 3x+5y?43200 Material: The come forwards of knockout quality is trammel to 120kg per day. A packet of Hi-Fibre inevitably 5g of concentrated character and a packet of Hi-Fibre positivist ineluctably 10g of concentrated fibre. thence the real(a) amount of concentrated fibre used to each one day is : 5x+10y grams 120kg=120000g thus 5x+10y?120 000 Market pull off out: The minimum number of each type of concentrated fibres packets that must be produced in each day is 2500 packets thereof x ? 2500, y?2500 w arehousing: The storage area heap abbreviate a maximal of 12000 packets so daily return cannot slip by this figure.

Therefore x+y?12000 Objective use of goods and services: Let P be the profit in pence each day from the trade of Hi-Fibre and Hi-Fibre Plus produced in each day; where P is in pence Therefore P=12x+15y Graph: Vertices: A: the orchestrate are (2500,2500) B: is at the mathematical product of x=2500 and 3x+5y=432000 Therefore the ordain of B are (2500,7140) C: is at the intersection of x+y=12000.a and 3x+5y=43200b a*3 3x+3y=36000c b-c 2y=7200 y=3600 substitute in a x=8400 Therefore the coordinate of C are (8400,3600) D: is at the intersection of y=2500 and x+y=12000 Therefore the coordinate of D are (9500,2500) best Solution: P(A)=12p*2500 + 15p*2500 =67500p P(B)=12p*2500+15p*7140=137100p P(C)=12p*8400+15p*3600=154800p P(D)=12p*9500+15p*2500=151500p Therefore the supreme profit each day is 154800p, the optimal number of Hi-Fibre and Hi-Fibre Plus produced per day is 8400 packets and 3600 packets. Task devil: a) If the optimal number of...If you wishing to get a extensive essay, order it on our website: Ordercustompaper.com

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