Question #237590

Use simplex method to maximize ð‘“ = 3ð‘¥ + 5ð‘¦ + 4ð‘§ subject to the conditions 2ð‘¥ + 3ð‘¦ ≤ 18 2ð‘¥ + 5ð‘¦ ≤ 10 3ð‘¥ + 2ð‘¦ + 4ð‘§ ≤ 15 and ð‘¥, ð‘¦, ð‘§ ≥ 0.

Expert's answer

One of the theorems of simplex method states that the solution of the linear problem exists at one of the edge points. In our case the region is bounded by 6 planes: , . It is possible to find such solution in Maple via the commands:

with(Optimization):

Minimize(-3*x-5*y-4*z,{2*x+3*y<=18,2*x+5*y<=10,3*x+2*y+4*z<=15,x>=0,y>=0,z>=0});

Since we want to reformulate the problem as the problem for minimum, the function must have the opposite sign.

The minimum point is at the intersection of planes . The minimum value of function is . Thus, the solution of the maximization problem is at the point . The value is .

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