📘 operations research

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

1. The Economic Order Quantity (EOQ) model is designed to find the optimal order quantity that minimizes the total inventory costs. 2. These total costs include two main components

1. **Problem Statement:** Calculate the safety stock, reorder point, and economic order quantity (EOQ) for a part with given demand, lead time, and cost parameters.

1. **State the problem:** We need to find the Economic Order Quantity (EOQ) for glass units, given the annual demand, ordering cost, and holding cost per unit. 2. **Given data:**

1. **State the problem:** We have three discount options for ordering skateboards with different quantity discounts and fixed order costs. We want to find the most cost-effective o

1. **Problem Statement:** We need to assign 3 jobs (A, B, C) to 4 machines (W, X, Y, Z) minimizing the total cost, given the cost matrix:

1. **State the problem:** We want to maximize the total profit from producing two components, C1 and C2, given constraints on costs, production capacity, and available resources.

1. Тодорхойлж байна: Диагоналийн аргаар хуваарилалт хийхэд i-р агуулахын ачаа дууссан үед дараагийн ачаа хуваарилах нүдийг олох шаардлагатай. 2. Диагоналийн аргын үндсэн зарчим: Ху

1. **Problem Statement:** Fill in the blanks for queuing system concepts, identify variables and events, complete probability tables, create CDFs, simulate interarrival and service

1. **Problem Statement:** A firm produces two products A and B. Each unit of A requires 2 kg raw material and 4 labor hours. Each unit of B requires 3 kg raw material and 3 labor h