Minimize Z = 2x + 4y

Subject to

x+y≥8

x+4y≥12

x≥3, y≥2

Maximize Z = 7x + 10y

Subject to

x+y≤30000      

y≤12000       

 x≥6000        

x≥y     

x, y≥0

Maximize Z = 3x + 4y

Subject to

2x+2y≤802x+4y≤120

Maximize Z = 10x + 6y

Subject to

 3x+y≤122x+5y≤34  x, y≥0

Maximize Z = 15x + 10y

Subject to

3x+2y≤802x+3y≤70  x, y≥0