Graph the system of constraints and find the value of x and y that maximize the objective function

Asked by maham237 @ 29/11/2020 in Mathematics viewed by 426 People

x>0. y>0. y<1/5x+2. 5>y+x. objective function: c=7x-3y

Answered by maham237 @ 29/11/2020

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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