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This ones a past exam question (6/10) which also appears in the BPP revision kit Q#25.
Cut & Stitch make two types of suits. W and L
Objective Function: 48W+40L
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Constraints:
Tailor’s time: 7W+5L<= 3500 hrs
Fabric: 2W+2L <= 1200 meters
W<=400
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A graph has been provided that indicates the optimal prod. point B, according to which W=250, L=350, this would get us the maximum contribution of 48(250)+40(350) = 26,000. I get this answer by solving it using the simultaneous equations method. However, if suppose W=400 while L=200 (which btw satisfies the constraints) would get a better contribution: 48(400)+40(200)=27,200, as of course the contribution gained from W is more than that of L, therefore doesn’t it make sense to produce W as much as possible to get more contribution. Comments & help plz.W = 400 and L = 200 does not satisfy the constraints!
To make that many would involved using 3,800 hours of tailors time, and there are only 3,500 hours available.Just looking at the feasible region tells us that the optimum can only possibly be at points A, B, C or D, and from the iso-profit line it is clearly at B.
(Incidentally you said you solved using the simultaneous equations method. There is no other method for finding the quantities at the relevant corner – you certainly must not try and read the answer from the graph itself!), and unless the examiner provides the graph (as in this question) then you must draw the graph – they will provide graph paper – otherwise you will get very few marks indeed.)
The free lecture on linear programming will help you.
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