Blending Problems: This is another large class of problems in which linear prograrnming is applied heavily. Blending is concerned with mixing differentmaterials called the constituents of the mixture (these may be chemicals, gasoline, fuels, solids, colors, foods, etc.) so that the mixture conforms tospecifications on several properties or charactenistics, To model a blending problem as an LP, the linearity assumptions must hold This implies that thevalue for a characteristic for the constituents in the mixtures are the weighted average of the values of that characteristic for the constituents in the mixture:the weights being the proportions of the constituents. As an example, consider a mixture consisting of 4 barrels of fuel 1 and 6 barrels of fuel 2 and supposethe characteristic of interest is the octane rating (Qc.R). Flinearity assumptions hold, the Oc.R of the mixture must be equal to (4 fimes the QcR of fuel 1+6 times the OcR of fuel 2)/(4 +6). These linearity assumptions hold to a reasonable degree of precision for many important characteristics of blends ofgasolines, of crude oils, of paints, of foods, etc. That's why linear programming is used extensively in optimizing gasoline blending, in the manufacture ofpaints, cattle feeds, beverages, etc. The decision variables ina blending problem are usually either the quantifies or the proportions of the constituents.Problem,Three liquid mixtures are to be designed as provided in the table below to contain a special chernical called "OptimOptum [7]45Availability [gallons]Cost (5/gallon]20Material008100015653070015003025MinimumOptim 7] Optim (%]253040MaximumRequired Amount(gallons]6001200900Selling Price ($/gallon)70105140Mixture455065Formulate an LP model to determine the production plan that maximizes profit.888

Question

Blending Problems: This is another large class of problems in which linear prograrnming is applied heavily. Blending is concerned with mixing differentmaterials called the constituents of the mixture (these may be chemicals, gasoline, fuels, solids, colors, foods, etc.) so that the mixture conforms tospecifications on several properties or charactenistics, To model a blending problem as an LP, the linearity assumptions must hold This implies that thevalue for a characteristic for the constituents in the mixtures are the weighted average of the values of that characteristic for the constituents in the mixture:the weights being the proportions of the constituents. As an example, consider a mixture consisting of 4 barrels of fuel 1 and 6 barrels of fuel 2 and supposethe characteristic of interest is the octane rating (Qc.R). Flinearity assumptions hold, the Oc.R of the mixture must be equal to (4 fimes the QcR of fuel 1+6 times the OcR of fuel 2)/(4 +6). These linearity assumptions hold to a reasonable degree of precision for many important characteristics of blends ofgasolines, of crude oils, of paints, of foods, etc. That's why linear programming is used extensively in optimizing gasoline blending, in the manufacture ofpaints, cattle feeds, beverages, etc. The decision variables ina blending problem are usually either the quantifies or the proportions of the constituents.Problem,Three liquid mixtures are to be designed as provided in the table below to contain a special chernical called &#34;OptimOptum [7]45Availability [gallons]Cost (5/gallon]20Material008100015653070015003025MinimumOptim 7] Optim (%]253040MaximumRequired Amount(gallons]6001200900Selling Price ($/gallon)70105140Mixture455065Formulate an LP model to determine the production plan that maximizes profit.888

Accepted Answer

Answered: Image /qna-images/answer/a1f52db5-e3e6-4259-b556-ed3eed1ed0f8.jpg