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svetlana [45]
3 years ago
13

Graph the system of constraints and find the value of x and y that maximize the objective function.. x>0. y>0. y<1/5x+2

. 5>y+x. objective function: c=7x-3y

Mathematics
2 answers:
Travka [436]3 years ago
5 0
X > 0 , everything to the right of the y-axis 
<span>y > 0 , everything above the x-axis </span>
So far you are in quadrant I of the x-y plane
<span>y<1/5x+2
</span><span>sketch a line leaning 45° to the left with a y-intercept of 2, shade in everything below that line 
</span>now our Objective Function is 
<span>C = 7x - 3y , which is a line with slope 7/3 </span>
<span>letting that line go through the origin, let it slide parallel to itself over the shaded region until you reach the farthest point from the origin. </span><span>
Here are the required values : 
c = 35; x = 5, y = 0</span>
iogann1982 [59]3 years ago
3 0

Answer: The value of x= 5

And the value of y =0.

Step-by-step explanation:

Since we have given that

Max\ c=7x-3y\\\\yy+x\\\\s.t.\  x>0\ y>0

As we can see from the graph, there are three points occurred in feasible region, which are as follows;

A(2.5,2.5)\\\\B(-10,0)\\\\C(5,0)

Now, we put the above three values in the objective function:

c=7x-3y\\\\Put\ A(2.5,2.5)\\\\c=7\times 2.5-3\times 2.5\\\\c=17.5-7.5\\\\c=10\\\\Similarly,\\\\Put\ B(-10,0)\\\\c=7\times -10-3\times 0\\\\c=-70\\\\Similarly,\\\\Put\ C(5,0)\\\\c=7\times 5-3\times 0\\\\c=35

Therefore, we can see that

At C(5,0) we get maximum value as c = 35.

Hence,  The value of x= 5

And the value of y =0.

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