Graph the system of constraints and find the value of x and y that maximize the objective function. constraints{×>0; y>0; y<1/5×+2; 5>y+× ojective function: c=7×-3y

Answer 1

To graph the system of constraints, we will first plot the line y < 1/5x + 2.

To do this, we will find and plot two points on the line:

When x = 0, y = 2.
When x = 5, y = (1/5)(5) + 2 = 3.

We can now plot these two points and draw a line through them.

Next, we will plot the line 5 > y + x. Again, we will find and plot two points for this line:

When x = 0, y = 5.
When y = 0, x = 5.

Plotting these two points and drawing a line through them, we have the following graph:

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The shaded region represents the feasible region satisfying all the constraints.

To find the value of x and y that maximize the objective function c = 7x - 3y, we need to find the point within the feasible region that gives the maximum value for this function.

By observing the graph, we can see that the feasible region is bounded by the line y = 1/5x + 2, and the maximum value of c = 7x - 3y will occur at one of the points of intersection between this line and the line 5 > y + x.

By solving the system of equations:

1/5x + 2 = y
5 = y + x

we can find the coordinates of the point of intersection.

From the second equation, we have x = 5 - y.

Substituting this into the first equation, we have:

1/5(5 - y) + 2 = y
(5 - y)/5 + 2 = y
(5 - y + 10)/5 = y
(15 - y)/5 = y
15 - y = 5y
6y = 15
y = 15/6 = 2.5

Substituting y = 2.5 into the second equation:

5 = 2.5 + x
x = 5 - 2.5 = 2.5

Therefore, the value of x and y that maximize the objective function c = 7x - 3y within the given constraints is x = 2.5 and y = 2.5.