📘 linear programming

1. **Problem Statement:** A farmer wants to minimize the daily cost of chicken feed using two types of feed, A and B.

1. **State the problem:** Minimize $$z = 2x_1 + 3x_2$$

1. **State the problem:** We want to minimize $$z = 2x_1 + 3x_2$$ subject to constraints:

1. **State the problem:** We want to maximize the objective function $$Z = 2x_1 + 10x_2$$

1. **Problem Statement:** A firm manufactures two products with profits of 3 and 5 per unit respectively. Each product requires processing time in two departments D1 and D2. Produc

1. **Problem Statement:** Minimize $$z = 4x_1 + 4x_2 + x_3$$ subject to: $$2x_1 + x_2 + 3x_3 \leq 2$$

1. **State the problem:** We need to minimize the cost function $$\text{Cost} = 1.80S + 2.20T$$ subject to the constraints: $$5S + 8T \geq 200$$

1. **State the problem:** We want to minimize the cost function $$P = 1.80S + 2.20T$$ subject to the constraints: $$5S + 8T \geq 200$$

1. **Stating the problem:** We want to maximize the power output function $$Z = 400X + 300Y$$ where $$X$$ and $$Y$$ represent the number of Monocrystalline and Polycrystalline sola

1. **Problem Statement:** We are given a linear programming problem to minimize the cost function $$\text{Cost} = 1.80S + 2.20T$$ subject to the constraints: $$5S + 8T \geq 200$$

1. **Problem Statement:** We have three loan products: Personal (P), Business (B), and Housing (H). Each requires certain resources (Officers, Compliance hours, Risk assessments) a

1. **Problem Statement:** Find the new optimal solution for the linear program when the objective function changes to:

1. **Problem Statement:** We want to maximize the profit from producing Alloy Gamma (x tons) and Alloy Delta (y tons) given constraints on raw materials Copper, Zinc, and Nickel.

1. **State the problem:** We are given a partial initial simplex tableau and asked to:

1. The problem is to understand how sensitivity analysis in linear programming helps determine the effect of changes in the objective function coefficients on the optimal solution.

1. **State the problem:** Minimize the objective function $$80x + 60y$$ subject to the constraints: $$2x + 6y \geq 18$$

1. **State the problem:** Minimize the objective function $$80x + 60y$$ subject to the constraints: $$2x + 6y \geq 18$$

1. **State the problem:** Minimize the objective function $$80x + 60y$$ subject to the constraints: $$2x + 6y \geq 18$$

1. **State the problem:** Minimize the objective function $$80x + 60y$$ subject to the constraints: $$2x + 6y \geq 18$$

1. **Problem 1: Maximize $30x + 50y$ subject to constraints:** $$3x + 4y \geq 12$$

1. **State the problem:** Maximize the objective function $$P = 8x + 6y$$