Write as a Vector Equality x+2y=48 , x+y=30 , 2x+y=50 , f=70x+30y

Problem

{[x+2*y=48],[x+y=30],[2*x+y=50],[ƒ=70*x+30*y])

Solution

1. Identify the variables and coefficients in the system of linear equations. The variables are x and y

2. Express the left-hand side of the first three equations as a linear combination of two vectors, using x and y as scalars.

3. Group the constants on the right-hand side into a single column vector.

4. Represent the objective function ƒ as a dot product of a coefficient vector and the variable vector.

5. Combine the equations into a single vector equality where the vector of variables is multiplied by a matrix of coefficients.

Final Answer

x*([1],[1],[2],[70])+y*([2],[1],[1],[30])=([48],[30],[50],[ƒ])

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