### Question Description

Solve the linear programming problem by the method of corners.

Find the minimum and maximum of *P* = 4*x* + 2*y* subject to

3x | + | 5y | ≥ | 20 |

3x | + | y | ≤ | 16 |

−2x | + | y | ≤ | 4 |

x ≥ 0, y ≥ 0. |

The minimum is *P* = at

*x*,

*y*) =

The maximum is

*P*= at

*x*,

*y*) =

## Final Answer

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3x+5y>=20------------(1)

-3x-y>=-16---------(2)

2x-y>=-4------------(3)

(1)+(2)

4y>=4

y>=1

**y max=1**

3x+5*1=20

x>=5

**x max=5**

**p max=4*5+2*1**

**=22**

**p min=4*0+2*0**

**=0**