📘 operations research

1. **Problem Statement:** We want to maximize the profit from producing two products, X and Y, using three machines M1, M2, and M3 with given time constraints.

1. **Problem statement:** Company X uses 4 units daily, 360 days/year. Ordering cost is 10 per order, carrying cost is 2 per unit. Current order size is 144 units.

1. **State the problem:** We need to fill the transportation table using the West-Left Corner Rule, which allocates supplies to demands starting from the top-left corner and moving

1. **Énoncé du problème :** Nous avons 3 entrepôts (A, B, C) avec des capacités respectives de 50, 60, et 50 unités.

1. **Linear Programming (LP)** is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear

1. **Problem Statement:** Precision Gears Ltd. needs to create an aggregate production plan for 3 months with given demands, capacities, and costs. We use the Transportation Table

1. Muammo: Eng kam xarajatlar usulida transport masalasining boshlang‘ich tayanch rejasini topish. 2. Formulalar va qoidalar:

1. **Problem Statement:** We have two machines C1 and C2 producing two grades of tyres A and B. Machine C1 produces 50 units of A and 30 units of B per hour, and machine C2 produce

1. Задача: Найти решение задачи оптимизации с использованием метода приоритетов на основе заданной матрицы стоимости и запасов. 2. Дано:

1. **Problem Statement:** (a) Define Operations Research (OR) and explain its growing importance.

1. **Problem Statement:** We need to solve a transportation problem using the stepping stone method. There are 3 factories (sources) with capacities 50, 100, and 150 units respecti

1. **State the problem:** We need to find the best product mix of products A, B, C, and D to maximize profit given constraints on preparatory and finisher machine hours.

1. **Problem Statement:** Calculate the optimal number of Solar Home Kits to purchase to maximize expected gross profit after advertising in (i) one newspaper and (ii) two newspape

1. **State the problem:** We want to determine the number of wrenches ($x$) and pliers ($y$) to produce to maximize profit given constraints on steel, machine hours, and demand.

1. **Problem Statement:** Solve the transportation problem using Vogel's Approximation Method (VAM) for the given cost matrix, supply, and demand.

1. **Problem 1 (Two marks):** Calculate the efficiency score of a Decision Making Unit (DMU) with inputs $x_1=4$, $x_2=3$ and outputs $y_1=8$, $y_2=6$ using the simple input-orient

1. **Problem Statement:** A manufacturer produces two products A and B using limited labour and raw materials.

1. **Problem Statement:** Maximize profit $P = x + 2y$ subject to constraints:

1. **Problem Statement:** We have four raw materials $R_1, R_2, R_3, R_4$ with constraints on their availability and usage, and costs associated with each. We want to construct a l

1. **Problem Statement:** Gabane Telecom Company produces two types of chargers: Type B and Type C. Each Type C requires 2 labor hours and 2 machine hours; each Type B requires 1 l

1. **Problem Statement:** Gabane Telecom Company produces two types of chargers: Type B and Type C. Each Type C charger requires 2 labor hours and 2 machine hours. Each Type B char