Answer:
Minimize C =[tex]13x + 3y[/tex]
[tex]12x + 14y \geq 21[/tex]
[tex]15x + 20y \geq 37[/tex]
and x ≥ 0, y ≥ 0.
Plot the the lines on the graph and find the feasible region
[tex]12x + 14y \geq 21[/tex] -- Blue
[tex]15x + 20y \geq 37[/tex] --- Green
So, the boundary points of feasible region are (-3.267,4.3) , (0,1.85) and (2.467,0)
Substitute the value in Minimize C
Minimize C =[tex]13x + 3y[/tex]
At (-3.267,4.3)
Minimize C =[tex]13(-3.267) + 3(4.3)[/tex]
Minimize C =[tex]-29.571[/tex]
At (0,1.85)
Minimize C =[tex]13(0) + 3(1.85)[/tex]
Minimize C =[tex]5.55[/tex]
At (2.467,0)
Minimize C =[tex]13(2.467) + 3(0)[/tex]
Minimize C =[tex]32.071[/tex]
So, the optimal value of x is -3.267
So, the optimal value of y is 4.3
So, the minimum value of the objective function is -29.571
