Use simplex method to maximize π = 3π₯ + 5π¦ + 4π§ subject to the conditions 2π₯ + 3π¦ ≤ 18 2π₯ + 5π¦ ≤ 10 3π₯ + 2π¦ + 4π§ ≤ 15 and π₯, π¦, π§ ≥ 0.
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:
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 .