📘 optimization

1. **Problem Statement:** We want to maximize the function $$f(x_1,x_2) = x_1^2 - x_1 x_2 + x_2^2 + 2x_1 + 4x_2 + 3$$ subject to $$-5 \leq x_1, x_2 \leq 5$$ using Particle Swarm Op

1. **Problem Statement:** Minimize the objective function subject to given constraints. Since the specific function and constraints are not provided, let's outline the general appr

1. **State the problem:** We need to find the cereal box dimensions that maximize the volume-to-surface-area ratio while meeting the constraints: - Volume between 3400 cm³ and 3425

1. **Nyatakan masalah:** Diberikan fungsi biaya bahan bakar tiga stasiun pembangkit thermal:

1. The problem is to find a subset of items from an Excel file whose total value sums to exactly 12121624.47, with the constraint that quantities can be reduced but not increased.

1. State the problem: Gru wants to fence a rectangular dog pen along his house, so no fence is needed on the house side. He needs to find the dimensions that minimize fencing cost

1. **State the problem:** A man is 12 miles south of a straight beach and needs to reach a point 20 miles east along the shore. He can travel by motorboat to some point on the beac

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.