What is the minimum value points of z=30x+40y subject of x+y<=140 x>=45 y>=32 20x+10y>=1500

9514 1404 393

  minimum z: 3050

Step-by-step explanation:

The attached graph shows the feasible region as a white space. The dashed lines at its edges are part of the solution set. The vertex closest to the origin is the one that minimizes z: (x, y) = (59, 32).

The minimum value of z is ...

  30·59 +40·32 = 3050

it has the same slope and a different y-intercept

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answer: d.) the total number of protons and neutrons is 15

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