It is requested to represent the following problems as linear programming models (PL). Should be Define decision variables, objective function and constraints. The restrictions are due number.
1.)The RECICLEX company operates a recycling center that collects four types of materials from waste solids and then treat them so they can amalgamate (treatment and amalgamation they constitute different processes) as salable products. Three degrees of that can be made amalgamated salable product, depending on the mixture of the materials used. Although there are some flexibility in the mix for each grade, the quality standards specify the quantity minimum or maximum of the materials allowed in that product grade. (This minimum amount or maximum is the weight of the material expressed as a percentage of the total weight for that grade of the product). These specifications are shown in the table below along with the cost of amalgamated and the sale price of each grade: Grade Specification Cost per pound amalgamated Sale price by pound of amalgamated $ 3.00 $ 8.50 Material 1: No more than 30% of the total Material 2: Not less than 40% of the total Material 3: No more than 50% of the total Material 4: Exactly 20% of the total $ 2.50 $ 7.00 Material 1: No more than 50% of the total Material 2: Not less than 10% of the total Material 4: Exactly 10% of the total Material 1: No more than 70% of the total $ 2.00 $ 5.50 The recycling center collects these solid waste materials from some regular sources, by what is in possibility of sustaining a stable rate to treat them. The following table shows the amounts available to collect and treat each week, as well as the cost of treatment for Each type of material. Material Pounds per week Cost of treatment by available pound 3,000 $3.00 2,000 $6.00 4,000 $4.00 1,000 $5.00 RECICLEX is owned by Mundo Limpio, an organization dedicated to managing 4 Ecological problems. RECICLEX earnings are used in full to help sustain the Clean World activities. Mundo Limpio has collected contributions and donations that add up to $ 30,000 per week, which he uses only to cover the total cost of treating materials for solid waste The Clean World Administration Council instructed RECICLEX to that distributes that money among the materials in such a way that at least half of the amount Available (pounds per week) of each material is collected and processed. Determine how the administration of RECICLEX should assign the materials to the grades of products to maximize the weekly profit and for this you must define: a) The variables of the model (score: 5%) b) The objective function (score: 15%) c) Model restrictions (score: 30%). 1.)The RECICLEX company operates a recycling center that collects four types of materials from waste solids and then treat them so they can amalgamate (treatment and amalgamation they constitute different processes) as salable products. Three degrees of that can be made amalgamated salable product, depending on the mixture of the materials used. Although there are some flexibility in the mix for each grade, the quality standards specify the quantity minimum or maximum of the materials allowed in that product grade. (This minimum amount or maximum is the weight of the material expressed as a percentage of the total weight for that grade of the product). These specifications are shown in the table below along with the cost of amalgamated and the sale price of each grade: Grade Specification Cost per pound amalgamated Sale price by pound of amalgamated $ 3.00 $ 8.50 Material 1: No more than 30% of the total Material 2: Not less than 40% of the total Material 3: No more than 50% of the total Material 4: Exactly 20% of the total $ 2.50 $ 7.00 Material 1: No more than 50% of the total Material 2: Not less than 10% of the total Material 4: Exactly 10% of the total Material 1: No more than 70% of the total $ 2.00 $ 5.50 The recycling center collects these solid waste materials from some regular sources, by what is in possibility of sustaining a stable rate to treat them. The following table shows the amounts available to collect and treat each week, as well as the cost of treatment for Each type of material. Material Pounds per week Cost of treatment by available pound 3,000 $3.00 2,000 $6.00 4,000 $4.00 1,000 $5.00 RECICLEX is owned by Mundo Limpio, an organization dedicated to managing 4 Ecological problems. RECICLEX earnings are used in full to help sustain the Clean World activities. Mundo Limpio has collected contributions and donations that add up to $ 30,000 per week, which he uses only to cover the total cost of treating materials for solid waste The Clean World Administration Council instructed RECICLEX to that distributes that money among the materials in such a way that at least half of the amount Available (pounds per week) of each material is collected and processed. Determine how the administration of RECICLEX should assign the materials to the grades of products to maximize the weekly profit and for this you must define: a) The variables of the model (score: 5%) b) The objective function (score: 15%) c) Model restrictions (score: 30%)
