Question 670640
Evaluate the objective function, {{{P}}}, at each vertex 
The maximum (if it exists) is the largest value of {{{P}}} at a vertex. The minimum is the smallest value of {{{P}}} at a vertex. 

 {{{P = 3x + y}}}

vertices are ({{{0}}},{{{0}}}), ({{{4}}}, {{{0}}}), ({{{3}}}, {{{4}}}), ({{{0}}}, {{{10}}}).

Put the vertices into a table: 


{{{vertex}}}|---{{{P}}}|

(0,0)|{{{3*0 + 0=0}}}| min|

(4, 0)|{{{3*4 + 0=12}}}| |

(3, 4)|{{{3*3 + 4=13}}}|max |

(0, 10)|{{{3*0 + 10=10}}}| |

so, the minimum is at the point ({{{0}}}, {{{0}}}) with a value of {{{P=0}}} and 

the maximum is at the point ({{{3}}}, {{{4}}}) and the value is {{{P=13}}}


{{{drawing( 600,600, -15, 15, -15, 15, 
         grid(0),locate( 0, 0, O( 0, 0 ) ),locate( 0, 10, A( 0, 10 ) ),locate( 4, 0, B( 4, 0 ) ),locate( 3, 4, C( 3, 4 ) ),
         line( 4, 0, 3, 4 ),line( 0, 0, 4, 0 ),line(0, 0, 0, 10 ),line( 0, 10, 3, 4 )
)}}}