This is year 2022. Electric Vehicles (EVS) can be seen on the roads in Pakistan. Currently, all EVs are imported and costs of these EVs are quite high. Government of Pakistan through its Electric Vehicle Policy 2020 had given many incentives to the auto industry to assemble EVs in Pakistan. Thanks to this policy, major car manufacturers in Pakistan have established manufacturing and assembling plants and very soon the first Made in Pakistan" Electric Vehicle will be seen on the roads of Pakistan. This will bring down the cost of EVs considerably and it is expected that by 2025, number of EVs in Pakistan will be increased 10 times. eCharge, is a private company, which started their business by setting up windfarms alongside Peshawar Islamabad Motorway to produce electricity using renewable sources (Wind). In the past one year, since EVs have arrived in Pakistan, they also ventured in the supply and installation of chargers for EVs. eCharge plan to install electric chargers both at public locations (e.g., highways, motorways etc.) as well as residential places. eCharge is mainly dealing with two different chargers i.e., "Speedx Charger" which is a fast charger normally installed at public locations and "sCharge which is a slow charger installed at residential places. Details of both these chargers are tabulated below. Type Number of Sockets Charging Time Price Speedx 2 30 minutes PKR 950,000 sCharger 1 1 hour PKR 250,000 *More than one car can be charged by a particular charger depending on number of sockets eCharge wants to develop a network of charging points at selected locations on Islamabad Peshawar motorway which is divided into 5 sections (Interchange is located at the junction of two sections). eCharge has acquired following data to plan for this network Potential Average Existing Location for Motorway Section Number of Charging daily cars Points new charging points Peshawar Ring Road to Charsada 32504 5 2 Charsada to KP Highway 24897 3 3 KP Highway to Mardan 31254 Mardan to Swabi 21587 1 Swabi to Islamabad 48976 3 3 4 3 6 Based on the data gathered from toll plazas, 01% of current motorway traffic is EVS, of which 20% normally charge outside their homes i.e., use public charging locations. Due to marketing challenges, eCharge has decided that they will only install private chargers at the premises of eCharge customers. These customers use electricity generated from windfarms setup by eCharge. The current customer base of eCharge alongside Islamabad - Peshawar motorway is tabulated below. Motorway Sections. eCharge Customers Peshawar Ring Road to Charsada 689 Charsada to KP Highway 513 KP Highway to Mardan 345 Mardan to Swabi 458 Swabi to Islamabad 626 eCharge has done an initial survey among its customers and estimates that only 1 % of these customers have a suitable place to install private chargers and also, they will be willing to install these chargers. Rana Fawad is the CEO of eCharge. He believes that this is the right time to enter this market and convert Islamabad-Peshawar motorway into an electric Motorway. Once this electric motorway is established, these charging points will be frequently used as the demand for EVs are expected to increase by 10 times, thus resulting in sizeable revenues for eCharge. He has secured a funding of PKR 15 million and wants to devise a strategy through which he can install maximum number of chargers to meet the future demand 1. Formulate eCharge problem of developing a network of chargers as an integer programming model. a. Clearly state decision variables (10 Points) b. Formulate Objective function (20 Points) C. Formulate constraints (30 Points) 2. Solve the model using Microsoft Excel Solver and report the solution (20 Points). 3. If Rana Fawad decides to only install Public Chargers and drop the idea of installing private chargers, how the mathematical formulation will change. Solve the updated model in Microsoft Excel Solver and report the solution. (20 points) This is year 2022. Electric Vehicles (EVS) can be seen on the roads in Pakistan. Currently, all EVs are imported and costs of these EVs are quite high. Government of Pakistan through its Electric Vehicle Policy 2020 had given many incentives to the auto industry to assemble EVs in Pakistan. Thanks to this policy, major car manufacturers in Pakistan have established manufacturing and assembling plants and very soon the first Made in Pakistan" Electric Vehicle will be seen on the roads of Pakistan. This will bring down the cost of EVs considerably and it is expected that by 2025, number of EVs in Pakistan will be increased 10 times. eCharge, is a private company, which started their business by setting up windfarms alongside Peshawar Islamabad Motorway to produce electricity using renewable sources (Wind). In the past one year, since EVs have arrived in Pakistan, they also ventured in the supply and installation of chargers for EVs. eCharge plan to install electric chargers both at public locations (e.g., highways, motorways etc.) as well as residential places. eCharge is mainly dealing with two different chargers i.e., "Speedx Charger" which is a fast charger normally installed at public locations and "sCharge which is a slow charger installed at residential places. Details of both these chargers are tabulated below. Type Number of Sockets Charging Time Price Speedx 2 30 minutes PKR 950,000 sCharger 1 1 hour PKR 250,000 *More than one car can be charged by a particular charger depending on number of sockets eCharge wants to develop a network of charging points at selected locations on Islamabad Peshawar motorway which is divided into 5 sections (Interchange is located at the junction of two sections). eCharge has acquired following data to plan for this network Potential Average Existing Location for Motorway Section Number of Charging daily cars Points new charging points Peshawar Ring Road to Charsada 32504 5 2 Charsada to KP Highway 24897 3 3 KP Highway to Mardan 31254 Mardan to Swabi 21587 1 Swabi to Islamabad 48976 3 3 4 3 6 Based on the data gathered from toll plazas, 01% of current motorway traffic is EVS, of which 20% normally charge outside their homes i.e., use public charging locations. Due to marketing challenges, eCharge has decided that they will only install private chargers at the premises of eCharge customers. These customers use electricity generated from windfarms setup by eCharge. The current customer base of eCharge alongside Islamabad - Peshawar motorway is tabulated below. Motorway Sections. eCharge Customers Peshawar Ring Road to Charsada 689 Charsada to KP Highway 513 KP Highway to Mardan 345 Mardan to Swabi 458 Swabi to Islamabad 626 eCharge has done an initial survey among its customers and estimates that only 1 % of these customers have a suitable place to install private chargers and also, they will be willing to install these chargers. Rana Fawad is the CEO of eCharge. He believes that this is the right time to enter this market and convert Islamabad-Peshawar motorway into an electric Motorway. Once this electric motorway is established, these charging points will be frequently used as the demand for EVs are expected to increase by 10 times, thus resulting in sizeable revenues for eCharge. He has secured a funding of PKR 15 million and wants to devise a strategy through which he can install maximum number of chargers to meet the future demand 1. Formulate eCharge problem of developing a network of chargers as an integer programming model. a. Clearly state decision variables (10 Points) b. Formulate Objective function (20 Points) C. Formulate constraints (30 Points) 2. Solve the model using Microsoft Excel Solver and report the solution (20 Points). 3. If Rana Fawad decides to only install Public Chargers and drop the idea of installing private chargers, how the mathematical formulation will change. Solve the updated model in Microsoft Excel Solver and report the solution. (20 points)