Question

the graph shows the feasible region for the system with constraints:
y ≤ 15
x + y ≤ 25
x + 2y ≥ 30
what are the vertices of the feasible region?
check all of the boxes that apply.
(0, 25)
(0, 15)
(10, 15)
(20, 5)
(25, 0)
(30, 0)
done
what is the minimum value of the objective function c = 4x + 9y?

Explanation:

Step1: Find intersection of $y=15$ and $x+y=25$

Substitute $y=15$ into $x+y=25$:
$x + 15 = 25 \implies x = 10$
Vertex: $(10,15)$

Step2: Find intersection of $y=15$ and $x+2y=30$

Substitute $y=15$ into $x+2y=30$:
$x + 2(15) = 30 \implies x = 0$
Vertex: $(0,15)$

Step3: Find intersection of $x+y=25$ and $x+2y=30$

Subtract $x+y=25$ from $x+2y=30$:
$(x+2y)-(x+y)=30-25 \implies y=5$
Substitute $y=5$ into $x+y=25$:
$x + 5 = 25 \implies x=20$
Vertex: $(20,5)$

Step1: Evaluate $C$ at $(0,15)$

$C=4(0)+9(15)=135$

Step2: Evaluate $C$ at $(10,15)$

$C=4(10)+9(15)=40+135=175$

Step3: Evaluate $C$ at $(20,5)$

$C=4(20)+9(5)=80+45=125$

Step4: Compare values

125 < 135 < 175

Answer:

(0, 15), (10, 15), (20, 5)

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For the minimum value of $C=4x+9y$ (assuming the typo is $9y$):