I need help with the constraint and how to solve the probelm on excel ### Problem 2 – Network ModelYou've just started a job at a company that produces and distributes products around Ohio. Your boss is struggling with the logistics of shipping your products in the most cost-effective way possible. She has tasked you with creating a network model in Excel to help her out. Your logistics network consists of three factories, two distribution centers, and two retail stores. The factories are located in Toledo, Cleveland, and Steubenville, OH. The distribution centers are located in Marion and Newark, OH. The retail locations are located in Columbus and Dayton, OH. A map of these nodes can be seen below:![Ohio Network Map](https://www.example.com/path_to_image.jpg)**Map Explanation:**The map illustrates the logistics network across Ohio with the following key points:- **Factories**: - **Toledo** (marked by a red dot in the northwest) - **Cleveland** (marked by a red dot in the northeast) - **Steubenville** (marked by a red dot in the east) - **Distribution Centers**: - **Marion** (marked by a red dot in the center-north) - **Newark** (marked by a red dot in the center-east) - **Retail Stores**: - **Columbus** (marked by a red dot in the center) - **Dayton** (marked by a red dot in the southwest)These locations will serve as the points in your network model to facilitate the efficient transportation and distribution of products within Ohio. ### Transportation Cost Optimization ProblemIn this problem, we are focusing on optimizing the transportation costs associated with shipping products between different cities. The table below details the transportation costs for a single unit of product between various source nodes and destination nodes.#### Cost Table| Source | Node 4 - Marion | Node 5 - Newark | Node 6 - Columbus | Node 7 - Dayton ||--------------|------------------|------------------|-------------------|------------------|| **Node 1 - Toledo** | $119 | $103 | - | - || **Node 2 - Cleveland** | $113 | $110 | - | - || **Node 3 - Steubenville** | $120 | $107 | - | - || **Node 4 - Marion** | - | - | $106 | $132 || **Node 5 - Newark** | - | - | $78 | $91 |Note: A dash ("-") indicates that no direct shipping cost is available between those nodes.### Problem DescriptionYour task involves optimizing the shipping schedule and costs between these nodes. There are three factories located in:- Toledo- Cleveland- SteubenvilleThe production capacities for these factories are as follows:- **Toledo:** 420 units per week- **Cleveland:** 470 units per week- **Steubenville:** 455 units per weekThe demand at the retail stores in different locations is also provided:- **Columbus:** 710 units per week- **Dayton:** 620 units per weekEach distribution center can handle a maximum of 670 units per week.### Problem-solving TaskFormulate a linear program to determine the optimal number of units your company should ship between these locations to minimize costs. Compute the associated cost and present your answers to two decimal places.### Instructions for Formulation1. **Decision Variables:** - Represent shipping from node $ i $ to node $ j $ using $ X_{ij} $. - Example: Shipping a unit from Node 1 (Toledo) to Node 2 (Cleveland) will be denoted as $ X_{12} $.2. **Objective Function:** - Minimize the total transportation cost. 3. **Constraints:** - Production

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costs associated with transporting a single unit of product between cities can be found in the table below: Destination Source Node 1 - Toledo Node 2 - Cleveland Node 3 - Steubenville Node 4 - Marion Node 5 - Newark Node 4 - Marion $119 $113 $120 Node 5 - Newark $103 $110 $107 Node 6 - Columbus Node 7 - Dayton $106 $78 $132 $91 Your boss tells you that the three factories (Toledo, Cleveland, Steubenville) each have different production capacities. They are 420, 470, and 455 units per week respectively. She also tells you that your retail stores have different levels of demand. Columbus has a demand of 710 units per week while Dayton has a demand of 620 units per week. Finally, each of the distribution centers can only handle 670 units each week. Formulate a linear program and solve to find the ideal number of units that your company should strive to ship between locations each week, and the associated cost of it. Round all answers to two decimal places. You'll notice that the sheet for this problem is blank. We are expecting you to be able to create a linear program from scratch, with proper formatting that you have learned so far in this class. We will expect decision variables to follow the correct naming convention. For example: the decision variable that represents shipping a unit from node 1, to node 2 would be written as: X12-

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...