Minimizing an equation that is subject to inequalities.

Question

I am unsure of how to minimize the equation

C = 3x + 7y

that is subject to 4x + y ≥38, 2x + y ≥30, x + 3y ≥30, x ≥ 0, y ≥ 0  

Thank you

Answer 1

If you graph each of the inequalities, you have to find the vertices of the section where all 5 of the equations are true. The points are:

(0,38)

(4,22)

(12,6)

(30,0)

Then you plug these points into the equation to see which one gives the minimum value.

C=3x+7y

3(0)+7(38) = 266

3(4)+7(22) = 166

3(12)+7(6) = 78

3(30)+7(0) = 90

78 is the minimum value