Modeling and resolution of Problem 1. An oil refinery is going to produce a new type of gasoline by mixing the 4 types of gasoline currently available, which have been obtained by processing differentModeling and resolution of Problem 1. An oil refinery is going to produce a new type of gasoline by mixing the 4 types of gasoline currently available, which have been obtained by processing different types of crude oil. There are four crudes of origin and they have different compositions. To simplify the problem, it is assumed that each type of gasoline has a different percentage of additives A, B and C. The following table indicates these percentages and the unit price for the four types of gasoline: additives Price Types Gas A B. C Gasoline Types 180 101043 two 30 30 403137010 twenty 47440 fifty 1037 Market demands dictate that the gasoline to be produced must contain at least 20% of additive A, at least 30% of B and at least 20% of C. In addition, it cannot contain more than 30% of type 1 gasoline nor more than 40% of type 2 gasoline. Determine the least expensive way to produce gasoline with these specifications. Start by defining the four variables in the problem by xi as the proportion of gasoline of type i in one liter of the mixture. The objective function is: minz= 431+312+473+374; which is the result of multiplying the vector of price by the vector of variables. The restrictions will be given by the product of the matrix of coefficients and the vector of the variables, as follows: 801+302+703+40420 Additive constraint A10 1+302+103+50430 Additive constraint B101+402+203+10420 Additive constraint x1+x2+x3+x4=100 Mix constraint x10.320.4 xiz Owith i=1,2,3,4 Open an Excel sheet to enter the data of the problem, leaving the cells corresponding to the results (the four variables and the objective function) blank, in addition to writing the restrictions to analyze whether it is a feasible solution. Questionnaire. Use the Excel Solver to model problem 2 of practice 1 . Taking into account that the objective of the company is to maximize its profit: 1 . How many of each product should you make? 2. What is the maximum profit that the company will achieve? 3. Which plants require to use all of their available capacity? Modeling and resolution of Problem 1. An oil refinery is going to produce a new type of gasoline by mixing the 4 types of gasoline currently available, which have been obtained by processing differentModeling and resolution of Problem 1. An oil refinery is going to produce a new type of gasoline by mixing the 4 types of gasoline currently available, which have been obtained by processing different types of crude oil. There are four crudes of origin and they have different compositions. To simplify the problem, it is assumed that each type of gasoline has a different percentage of additives A, B and C. The following table indicates these percentages and the unit price for the four types of gasoline: additives Price Types Gas A B. C Gasoline Types 180 101043 two 30 30 403137010 twenty 47440 fifty 1037 Market demands dictate that the gasoline to be produced must contain at least 20% of additive A, at least 30% of B and at least 20% of C. In addition, it cannot contain more than 30% of type 1 gasoline nor more than 40% of type 2 gasoline. Determine the least expensive way to produce gasoline with these specifications. Start by defining the four variables in the problem by xi as the proportion of gasoline of type i in one liter of the mixture. The objective function is: minz= 431+312+473+374; which is the result of multiplying the vector of price by the vector of variables. The restrictions will be given by the product of the matrix of coefficients and the vector of the variables, as follows: 801+302+703+40420 Additive constraint A10 1+302+103+50430 Additive constraint B101+402+203+10420 Additive constraint x1+x2+x3+x4=100 Mix constraint x10.320.4 xiz Owith i=1,2,3,4 Open an Excel sheet to enter the data of the problem, leaving the cells corresponding to the results (the four variables and the objective function) blank, in addition to writing the restrictions to analyze whether it is a feasible solution. Questionnaire. Use the Excel Solver to model problem 2 of practice 1 . Taking into account that the objective of the company is to maximize its profit: 1 . How many of each product should you make? 2. What is the maximum profit that the company will achieve? 3. Which plants require to use all of their available capacity