📘 optimization

1. **Problem 1: Minimize the function** Given the function to minimize:

1. **Problem 1: Minimize the function** $$f(x,y) = 25(3x - 1)^3 + 4xy + y^2$$ starting at point $$x_1 = (0.4, -0.8)$$ with tolerance $$\varepsilon = 10^{-1}$$ using Newton's method

1. Stating the problem: We want to maximize the objective function $$Z = 20000x + 25000y$$ subject to the constraints:

1. **State the problem:** The company produces three components A, B, and C.