Question

the vertices of a feasible region are (14, 2), (0, 9), (6, 8), and (10, 3). what is the maximum value of the objective function ( p ) if ( p = 180x + 250y )?
( \bigcirc ) 2,940
( \bigcirc ) 3,020
( \bigcirc ) 3,080
( \bigcirc ) 3,250

Explanation:

Step1: Evaluate P at (14,2)

Substitute $x=14, y=2$ into $P=180x+250y$
$P = 180(14) + 250(2) = 2520 + 500 = 3020$

Step2: Evaluate P at (0,9)

Substitute $x=0, y=9$ into $P=180x+250y$
$P = 180(0) + 250(9) = 0 + 2250 = 2250$

Step3: Evaluate P at (6,8)

Substitute $x=6, y=8$ into $P=180x+250y$
$P = 180(6) + 250(8) = 1080 + 2000 = 3080$

Step4: Evaluate P at (10,3)

Substitute $x=10, y=3$ into $P=180x+250y$
$P = 180(10) + 250(3) = 1800 + 750 = 2550$

Step5: Compare all P values

Compare 3020, 2250, 3080, 2550 to find the maximum.

Answer:

3,080