Which term best describes the solution of the situation represented by the system of inequalities? (assume that x is greather than or equal to 0 and y is greater than or equal to 0)

3x+4y is less than or eaual to 8

2x+4y is less than or equal to 6
f(x, y)=x+y

a. alternate optimal solutions
b. one optimal solution
c. unbounded
d. infeasible

The system of Inequality given here is

  1. →x≥0

  2.→y≥0

  3.→3x+4y≤8

   4.→2x+4y≤6

f(x,y)=x+y

Drawing the Inequality on the Coordinate plane and obtaining the feasible points

And Feasible Points are

1.→(0,1.5)

2.→(0,0)

3.→(2.667,0)

4.→(2,0.5)

→f(0,1.5)=0+1.5=1.5

→f(0,0)=0+0=0

→f(2.667,0)=2.667+0=2.667

→f(2,0.5)=2+0.5=2.5

⇒There is one Optimal Solution obtained at Point (2.667,0).

Option B

One optimal solutions

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