Problem #2 Primal Formulation-LP Model 1 Hardrocker electronics, a dishwasher manufacturer, has decided to produce and sell two different types of dishwasher sets, standard (product 1) and deluxe (product 2). Product 1 will give a profit of $300 per unit and Product 2 a profit of $500 per unit. Hardrocker has one production plant with four departments: Molding, Soldering, Assembly and Inspection. Each dishwasher set is processed in sequence through these four departments. Each department has a limited capacity given by a maximum number of working hours per year. We assume Hardrocker electronics can sell all the dishwasher sets they are able to produce. Formulate an LP Model in order to determine the optimal production quantities for maximizing profit. Dept. Capacity in hours per year Table 1: Data for Primal LP Hours used by one unit Hours used by one unit of product 1 of product 2 1 5 1 1 2 1 Molding Soldering Assembly Inspection 4000 1200 2000 5000 2 5 Dual Formulation-LP Model 2 Hardrocker Electronic is planning to halt production for 1 year due to supply chain issues. Formulate a linear programming model in order to come up with a pricing scheme ($/Unit of Resource) for each resource assuming the resources can be sold as bundles of capacity to an external buyer for one year for producing different set of goods. The decision variable in this problem would be the following: YA = Price ($) of 1 hour of Molding Ya = Price ($) of 1 hour of Soldering Y3 = Price ($) of 1 hour of Assembly Y4 = Price ($) of 1 hour of Inspection The pricing of the resources or the worth of the resource would need to be assigned such that Hardrocker electronics can recover at least what they would be worth if they had continued producing and selling Product 1 and Product 2. And so, Hardrocker electronics wants to ensure that they make the same relative profit by leasing out their resources as if they had continued to sell Product 1 and Product 2 for the one year. The constraints for the Dual LP model would need to accomplish the following: 1. Hardrocker electronics would like to make at least $300 for every 1 Hour of Molding, 1 Hour of Soldering, 2 Hour of Assembly and 2 Hour of Inspection had the production of Product 1 continued. 2. Hardrocker electronics would like to make at least $500 for 5 Hours of Molding, 1 Hour of Soldering, 1 Hour of Assembly and 5 Hour of Inspection had the production of Product 2 continued. The goal/objective of the Dual LP model will be to determine the lowest possible price for each resource on a price per unit basis that could be offered to an external buyer such that at minimum same earnings are made in total rental fees as if they had continued their production operations and proceeded to sell Product 1 and Product 2. Note: Data for Dual LP formulation can also be found in Table 1. Problem #2 Primal Formulation-LP Model 1 Hardrocker electronics, a dishwasher manufacturer, has decided to produce and sell two different types of dishwasher sets, standard (product 1) and deluxe (product 2). Product 1 will give a profit of $300 per unit and Product 2 a profit of $500 per unit. Hardrocker has one production plant with four departments: Molding, Soldering, Assembly and Inspection. Each dishwasher set is processed in sequence through these four departments. Each department has a limited capacity given by a maximum number of working hours per year. We assume Hardrocker electronics can sell all the dishwasher sets they are able to produce. Formulate an LP Model in order to determine the optimal production quantities for maximizing profit. Dept. Capacity in hours per year Table 1: Data for Primal LP Hours used by one unit Hours used by one unit of product 1 of product 2 1 5 1 1 2 1 Molding Soldering Assembly Inspection 4000 1200 2000 5000 2 5 Dual Formulation-LP Model 2 Hardrocker Electronic is planning to halt production for 1 year due to supply chain issues. Formulate a linear programming model in order to come up with a pricing scheme ($/Unit of Resource) for each resource assuming the resources can be sold as bundles of capacity to an external buyer for one year for producing different set of goods. The decision variable in this problem would be the following: YA = Price ($) of 1 hour of Molding Ya = Price ($) of 1 hour of Soldering Y3 = Price ($) of 1 hour of Assembly Y4 = Price ($) of 1 hour of Inspection The pricing of the resources or the worth of the resource would need to be assigned such that Hardrocker electronics can recover at least what they would be worth if they had continued producing and selling Product 1 and Product 2. And so, Hardrocker electronics wants to ensure that they make the same relative profit by leasing out their resources as if they had continued to sell Product 1 and Product 2 for the one year. The constraints for the Dual LP model would need to accomplish the following: 1. Hardrocker electronics would like to make at least $300 for every 1 Hour of Molding, 1 Hour of Soldering, 2 Hour of Assembly and 2 Hour of Inspection had the production of Product 1 continued. 2. Hardrocker electronics would like to make at least $500 for 5 Hours of Molding, 1 Hour of Soldering, 1 Hour of Assembly and 5 Hour of Inspection had the production of Product 2 continued. The goal/objective of the Dual LP model will be to determine the lowest possible price for each resource on a price per unit basis that could be offered to an external buyer such that at minimum same earnings are made in total rental fees as if they had continued their production operations and proceeded to sell Product 1 and Product 2. Note: Data for Dual LP formulation can also be found in Table 1