Maximize:
\[ 4x_1 + 2x_2 + 4x_3 + 6x_4 + 7x_5 \]

Subject to:
\[ 8x_1 + 6x_2 + 8x_3 + 8x_4 + 10x_5 \leq 200 \]
\[ 2x_1 + x_2 + 2x_3 + 3x_4 + 4x_5 \leq 60 \]
\[ 6x_1 + 4x_2 + 4x_3 + 6x_4 + 8x_5 \leq 120 \]
\[ 6x_1 + 3x_2 + 4x_3 + 6x_4 + 6x_5 \leq 100 \]

With constraints:
\[ x_1 \geq 0 \]
\[ x_2 \geq 0 \]
\[ x_3 \geq 0 \]
\[ x_4 \geq 0 \]
\[ x_5 \geq 0 \]

This is a Linear Programming problem where the objective is to maximize a function subject to constraints. This can be solved using methods like the simplex method or softwares like MATLAB or Python's scipy.

Explanation:

The given problem is a Linear Programming problem where you're trying to maximize a linear function (Max = 4x1 + 2x2 + 4x3 + 6x4 + 7x5) subject to a set of linear constraints (the inequalities provided). In linear programming, you typically try to find values of the variables (x1, x2, ..., x5 in this case) to maximize or minimize the objective function (Max in this case). The constraints (inequalities) limit the solution space within which the solution (values of x1, x2, ..., x5) must lie. To solve this, you can use techniques like the simplex method or through softwares like MATLAB or Python's scipy.

Learn more about Linear Programming here:

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