3. Consider the following problem. Maximize Z = 2x1 + 7x2 + 4x3 subject to x1 + 2x2 + x3 ≤ 10 3x1 + 3x2 + 2x3 ≤ 10 x1, x2, x3 ≥ 0. 1 (a) (points: 4) Construct the dual problem for this primal problem. (b) (points: 2) Use the dual problem to demonstrate that the optimal value of Z for the primal problem cannot exceed 25.

Prove the converse of the pythagorean theorem using similar triangles. the converse of the pythagorean theorem states that when the sum of the squares of the lengths of the legs of the triangle equals the squares length of the hypotenuse, the triangle is a right triangle. be sure to create and name the appropriate geometric figures.