1. Work out or solve 3x + 5y < 15 graphically

 Answer

Write the known constraint in the form of equation, that is 3x + 5y = 15

Put x=0, then value of y=3

Put y=0, then value of x=5

Thus, the coordinates are (0, 3) and (5, 0). Hence these points are joined to get a straight line as present in the graph.

Place x=0, y=0 in the given constraint then

0<15, the condition is true. (0, 0) is solution closer to origin. Thus shade the region below that line, which is referred to the feasible region.

2. Work out or Solve 3x + 5y >15

Solution

Write the given constraint in the form of equation, that is 3x + 5y = 15

Place x=0, then y=3

Place y=0, then x=5

Now the coordinates are (0, 3) and (5, 0)

Place x =0, y =0 in the known constraint, the condition becomes false i.e. 0 > 15 is false.

Consequently the region does not have (0, 0) as solution. The feasible region stays on the exterior part of the line as presented in the graph.

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