Problem program linear

[Cerb189]

G.C.R. produces two types of food: A and B. For producing 1 kg of A, we need to combine 700 gr of the product X and 300 gr of the product Y. And for producing 1 kg of B, we need to combine 300 gr of the product X and 700 gr of the product Y. The total demand for A is 100 kg and for B is 120 kg. The time required to separate A and B in the product X is 5 hours per kg, and in the product Y is 3 hours per kg, where the total time we have to separate them is 950 hours. The maximum quantity of the product X and Y we can buy is 150 kg and 130 kg respectively, and their cost per kg is 2 and 3 euros. With this information, the manager of the company has developed the following linear programming model and has solved it.


I believe

Min 5x+3y
0,7x + 0,3 y less or equal to 100
0,3 x + 0,7 y less or equal to 120


Mmh but I don’t know. What do you suggest?

[HallsofIvy]

G.C.R. produces two types of food: A and B. And for producing 1 kg of B, we need to combine 300 gr of the product X and 700 gr of the product Y. The total demand for A is 100 kg and for B is 120 kg. The time required to separate A and B in the product X is 5 hours per kg, and in the product Y is 3 hours per kg, where the total time we have to separate them is 950 hours. The maximum quantity of the product X and Y we can buy is 150 kg and 130 kg respectively, and their cost per kg is 2 and 3 euros. With this information, the manager of the company has developed the following linear programming model and has solved it.

First, I would NOT say that A, B, X, and Y are "types" of food because, in order to form equations, they need to be NUMBERS! So I would say "let A and B be the number of kilograms of these types of food produced, let X and Y be the number of kilograms of these two products required".

"The total demand for A is 100 kg and for B is 120 kg."
So A<= 100 and B<= 120.

"For producing 1 kg of A, we need to combine 700 gr of the product X and 300 gr of the product Y."
So A= .7X+ .3Y.

"For producing 1 kg of B, we need to combine 300 gr of the product X and 700 gr of the product Y."
So B= .3X+ .7Y.

"The maximum quantity of the product X and Y we can buy is 150 kg and 130 kg respectively."
So X<= 150 and Y<= 130.

"The time required to separate A and B in the product X is 5 hours per kg, and in the product Y is 3 hours per kg, where the total time we have to separate them is 950 hours."
I may be misunderstanding what is meant by "separate A and B".
This might be 5X+ 3Y<= 950.

Now, what is the purpose of this? What is it you want to minimize? I don't see that stated anywhere. You give, in your answer, "5x+ 3y" but that's the time required to "separate" X and Y and you don't need to minimize that, just make sure it is less than or equal to 950.