Question

To use the simplex method to maximize the given function, assume all variables are nonnegative. Maximize f = 3x + 18y subject to the following constraints:

14x + 7y ≤ 49
5x + 5y ≤ 70
Your objective is to find the values of x and y that maximize f.

Answer 1

The Simplex method is used to maximize the objective function f = 3x + 18y with given constraints by plotting the constraints, identifying the feasible region, finding corner points, and testing these points in the function to find the maximum value.

Step-by-step explanation:

To maximize the function f = 3x + 18y with the constraints 14x + 7y ≤ 70 and 5x + 5y ≤ 70, the Simplex method can be applied. Start by converting the constraints into equations by introducing slack variables. Plot these constraints on a graph, label the axes, and identify the feasible region. Find the corner points of the feasible region and substitute these into the objective function f to determine the maximum value. Ensure all variables are nonnegative throughout the process.