Answer:
Option C.
Step-by-step explanation:
The given objective function is
[tex]P=15x+20y[/tex]
Subject to constraints.
[tex]x+y\leq 15[/tex] .... (1)
[tex]2x+y\leq 25[/tex] .... (2)
[tex]x\ge 0,y\ge 0[/tex]
The related equations of given inequalities are
[tex]x+y=15[/tex]
[tex]2x+y=25[/tex]
Table of values:
For inequality (1).
x y
0 15
15 0
For inequality (2).
x y
0 25
12.5 0
Plot these ordered pairs and draw the related lines.
Check both inequalities by (0,0).
[tex](0)+(0)\leq 15\Rightarrow 0\leq 15[/tex] True
[tex]2(0)+(0)\leq 25\Rightarow 0\leq 25[/tex] True
In means (0,0) included in shaded region of both inequalities. [tex]x\ge 0,y\ge 0[/tex] means first quadrant.
From the below graph it is clear that the vertices of feasible region are (0,0), (0,15), (10,5) and (12.5,0).
Point P=15x+20y
(0,0) P=15(0)+20(0)=0
(0,15) P=15(0)+20(15)=300
(10,5) P=15(10)+20(5)=250
(12.5,0) P=187.5+20(0)=0
The maximum value of objective function is 300 at x=0 and y=15.
Therefore, the correct option is C.
