📘 operations research

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

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

1. The problem is to maximize or minimize a linear objective function subject to a set of linear inequalities or equations called constraints. 2. A typical linear programming probl

1. **Problem statement:** We have a linear programming (LP) problem (P) and its integer programming (IP) version with integer constraints on $x_1, x_2$. 2. **Part (a):** What can b

1. **Problem statement:** We analyze the multi-objective optimization problem (P) with objectives $$w_1 = -2x_1 + x_2$$ and $$w_2 = -x_1 - 3x_2$$ subject to constraints $$x_1 + x_2

1. **Problem Statement:** We have a transportation problem with origins San Jose, Las Vegas, Tucson and destinations Los Angeles, San Francisco, San Diego. The goal is to minimize

1. **Problem Statement:** A company transports units from three factories (F1, F2, F3) to four warehouses (W1, W2, W3, W4). Given transportation costs, supplies, demands, and a fea

1. **State the problem:** We have an annual demand $D=5000$ packs, ordering cost per order $S=12000$, holding cost per pack per year $H=4000$, and lead time of 3 weeks. We need to

1. **State the problem:** Calculate the Economic Order Quantity (EOQ), ordering frequency, total costs, and reorder level for an inventory system with given demand, ordering cost,

1. **State the problem:** We want to determine how many units of products A and B to produce weekly to maximize profit.

1. **Problem statement:** We have a duplicating machine with a Poisson service rate of mean $\mu = 10$ jobs/hour and arrivals at rate $\lambda = 5$ jobs/hour over an 8-hour workday

1. **State the problem:** Mossaic Tiles, Ltd. wants to maximize profit by deciding how many batches of large tiles ($x$) and small tiles ($y$) to produce weekly, subject to constra

1. **Problem 1: Minimizing Transportation Cost for Beer Distribution** We have 4 depots (Chilanga Freedom, Chelston Green, George Compound, Jack Compound) and 4 beer brands (Chat B

1. **Problem 1: Maximize Z = 2x_1 + x_2** subject to $$x_2 \leq 10$$

1. The MODI (Modified Distribution) method is used in transportation problems to find the optimal solution minimizing transportation cost. 2. Start with an initial feasible solutio

1. **Problem:** Find the initial basic feasible solution for the transportation problem using Vogel's Approximation Method (VAM) and then find the optimum solution. 2. **Given Data

1. **Problem:** Find the initial basic feasible solution for the transportation problem using Vogel's Approximation Method (VAM) and then find the optimum solution using the MODI m

1. The MODI (Modified Distribution) method is used to find the optimal solution for transportation problems after obtaining an initial feasible solution. 2. First, calculate the **

1. The MODI method (Modified Distribution method) is used in transportation problems to find the optimal solution that minimizes transportation cost. 2. Start with a basic feasible

1. **Problem Statement:** Find the initial basic feasible solution (IBFS) using Vogel's Approximation Method (VAM) and then find the optimum solution for the transportation problem

1. The problem asks about the meaning of a negative $Z_j - C_j$ value in a simplex table during a maximization problem. 2. In the simplex method, $Z_j$ represents the total contrib