Find the maximum and minimum values of the given objective function on the indicated feasible region.
M = 150 − x − y
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To find the maximum and minimum values of the objective function M = 150 - x - y on the indicated feasible region, we need to follow these steps:
1. Identify the feasible region: The feasible region represents the set of all possible values of x and y that satisfy all the constraints given in the problem. The feasible region may be defined by a set of linear inequalities or other conditions specified in the problem.
2. Determine the boundary of the feasible region: The boundary of the feasible region is the set of points where at least one constraint is met as an equality. To find the boundary, set each constraint in the problem equal to zero and solve for x and y.
3. Identify the critical points: Critical points occur within the feasible region where the objective function reaches its maximum or minimum. These points can be found by setting the partial derivatives of the objective function with respect to x and y equal to zero and solving for x and y.
4. Evaluate the objective function at the critical points and boundary points: Once the critical points and boundary points are identified, substitute the x and y values into the objective function to find the corresponding values of M.
5. Compare the values: Compare the calculated values of M at the critical points and boundary points to find the maximum and minimum values of the objective function within the feasible region.
Keep in mind that without specific constraints or the feasible region defined, it is not possible to provide an exact solution for the maximum and minimum values.