Question

What is the maximum value of the objective function, P, with the given constraints? P=15x+20y

Answer 1

Answer:

Option C.

Step-by-step explanation:

The given objective function is

$P=15x+20y$

Subject to constraints.

$x+y\leq 15$            .... (1)

$2x+y\leq 25$            .... (2)

$x\ge 0,y\ge 0$

The related equations of given inequalities are

$x+y=15$

$2x+y=25$

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).

$(0)+(0)\leq 15\Rightarrow 0\leq 15$  True

$2(0)+(0)\leq 25\Rightarow 0\leq 25$    True

In means (0,0) included in shaded region of both inequalities. $x\ge 0,y\ge 0$ 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.