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Question 1151283: An air force is experimenting with three types of bombs P, Q, and R in which three kinds of Explosive viz, A, B and C will be used. Taking the various factors into consideration, it has been decided to use the maximum 600 kg of explosive A, at least 480 kg of explosive B and Exactly 540 of explosive C. Bomb P requires 3,2,2 kg of A,B,C respectively. Bomb Q requires 1, 4, 3 kg of A, B, and C respectively. Bomb R requires 4, 2, 3 kg of A, B, C respectively. Now bomb P will give the equivalent of 2 ton explosive, bomb Q will give 3 ton explosive and bomb R will give 4 ton explosive. Under what production schedule can the Air Force make the biggest bang?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i interpretecd this problem two ways.
the first way was that exactly 600 kg of explosive A, at least 480 kg of explosive B, and exactly 540 kg of explosive C were used.
the result of that analysis is shown below.
the second was was that a maximum of 600 kg of explosive A, at least 480 kg of explosive B, and exactly 540 kg of explosive C were used.
the result of that analysis is shown below.
the problem in the analysis was the interpretation of "decided to use the maximum 600 kg of explosive A".
the first interpretation assumes that exactly 600 kg of explosive A was used.
the second interpretation assumes that a maximum of 600 kg of explosive A was used, implying that less than 600 could be used.
your objective function is:
e = 2x + 3y + 4z
this is what you want to maximize.
assumption 1 maximizes at 645 tons of explosive.
assumption 2 maximizes at 660 tons of explosive.
the constraint equations are the same with the exception that:
assumption 1 assumes 3x + y + 4z = 600
assumption 2 assumes 3x + y + 4z <= 600
not forcing explosive A to be equal to 600 kg frees up the equations to maximize with or without explosive A.
that led to 0 numbers of bomb type P rather than 45 that was based on assumption 1.
my inclination is to go with assumption 1, but i included assumption 2 just in case my assumption of interpretation 1 was wrong.
the simplex method tool used can be found at https://www.zweigmedia.com/RealWorld/simplex.html
assumption 1 results say to use 45 type P, 45 type Q, and 105 type R bombs.
assumption 2 results say to use 0 type P, 60 type Q, and 120 type R bombs.
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