Question 1151283
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.


<img src = "http://theo.x10hosting.com/2020/011601.jpg" >


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.


<img src = "http://theo.x10hosting.com/2020/011601.jpg" >


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 <a href = "https://www.zweigmedia.com/RealWorld/simplex.html" target = "_blank">https://www.zweigmedia.com/RealWorld/simplex.html</a>


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.