Use the simplexe method to man the given function. Asume al variabled Maximzet-5x+6y subject to X+2y<10
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![**Title: Maximizing a Linear Function Using the Simplex Method**
**Objective:**
To maximize the given linear function assuming all variables are non-negative.
**Problem Statement:**
Maximize the function:
\[ f = 5x + 6y \]
**Subject to the constraints:**
1. \( x + 2y \leq 10 \)
2. \( x + y \leq 7 \)
**Solution Variables:**
- \((x, y) = (\quad, \quad)\)
- \( f = \)
**Explanation:**
This exercise involves using the Simplex Method, a popular algorithm for numerical optimization in linear programming. The objective is to find the maximum value of the linear function \( f = 5x + 6y \) given the specified constraints on \( x \) and \( y \). The region defined by the constraints is a convex polytope, and the Simplex Method will navigate the vertices of this region to find the optimum solution.
**Steps to Solve:**
1. Graph the region of feasible solutions as defined by the constraints.
2. Identify the vertices (corner points) of the feasible region.
3. Evaluate the objective function \( f = 5x + 6y \) at each vertex.
4. Select the vertex that provides the highest value of \( f \).
This mathematical approach allows for the determination of optimal allocation or outcomes in scenarios constrained by linear inequalities.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a799525-bc02-4aa7-a724-19d6c1834605%2F7377d251-83ca-4b3e-8cbd-b209679b0307%2Fu9ehpm_processed.jpeg&w=3840&q=75)
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