A large oil company produces three grades of gasoline: regular,unleaded,and super-unleaded.To produce these gasolines,equipment is used which requires as input certain amounts of each of the three grades of gasoline.To produce a dollar's worth of regular requires inputs of worth of regular,$0.18 worth of unleaded,and $0.17 worth of super-unleaded.To produce a dollar's worth of unleaded requires inputs of $0.14 worth of regular,
Worth of unleaded,and
Worth of super-unleaded.To produce a dollar's worth of super-unleaded requires inputs of
Worth of regular,$0.17 worth of unleaded,and $0.11 worth of super-unleaded.In addition,the oil company has final demands for each of the different grades of gasoline.Find the coefficient matrix that would be used in determining the total output of each grade of gasoline.

Question

A large oil company produces three grades of gasoline: regular,unleaded,and super-unleaded.To produce these gasolines,equipment is used which requires as input certain amounts of each of the three grades of gasoline.To produce a dollar's worth of regular requires inputs of  worth of regular,$0.18 worth of unleaded,and $0.17 worth of super-unleaded.To produce a dollar's worth of unleaded requires inputs of $0.14 worth of regular, 
Worth of unleaded,and 
Worth of super-unleaded.To produce a dollar's worth of super-unleaded requires inputs of 
Worth of regular,$0.17 worth of unleaded,and $0.11 worth of super-unleaded.In addition,the oil company has final demands for each of the different grades of gasoline.Find the coefficient matrix that would be used in determining the total output of each grade of gasoline.

Quizplus · Accepted Answer

The coefficient matrix can be found by arranging the input amounts for each grade of gasoline in a matrix. The rows represent each grade of gasoline and the columns represent the input amounts of each grade of gasoline. Using the given input amounts, the coefficient matrix would be:

A = 
[11, 0.18, 0.17]
[0.14, 11, 0.12]
[11, 0.17, 0.11]

Therefore, the best choice is A.

A Large Oil Company Produces Three Grades of Gasoline: Regular,unleaded,and