by graphing the system of constraints find the values of x and y that minimizes the objective function
x+2y>8
x>2
y>0
>=greater than or equal to
my answer was 0,10 am i right?
no idea. what is the objective function?
To graph the system of constraints, we need to plot the inequalities on a coordinate plane. Then, we can find the region that satisfies all the constraints and determine the values of x and y that minimize the objective function.
1. Start by graphing the first inequality, x + 2y > 8:
a. Draw the line x + 2y = 8 (convert the inequality into an equation).
b. Choose a point not on the line, like (0,0), and check if it satisfies the inequality. If it does, shade the region containing (0,0). If it doesn't, shade the other region.
2. Now graph the second inequality, x > 2:
a. Draw the vertical line x = 2.
b. Shade the region to the right of the line since it satisfies the inequality.
3. Lastly, graph the third inequality, y > 0:
a. Draw the horizontal line y = 0 (the x-axis).
b. Shade the region above the line since it satisfies the inequality.
The region where all the shaded regions overlap represents the feasible region that satisfies all the constraints.
Now, to find the values of x and y that minimize the objective function, we need to find the coordinates of the corner points within the feasible region.
In this case, the feasible region has an infinite number of corner points along the line x + 2y = 8. To find the specific points, we can either:
- Use the equation x + 2y = 8 and set x equal to 2 or y equal to 0, then find the corresponding value for the other variable.
- Or, we can use the extreme values of the shaded region on that line closest to the origin. In this case, the two closest extreme points on the line to the origin are (2,3) and (4,2).
Now we compare the objective function value at these corner points:
- (2,3) yields 2 + 2(3) = 8
- (4,2) yields 4 + 2(2) = 8
Since both points have the same objective function value, any point along that line will yield the same value. Hence, there is no single pair of x and y that minimizes the objective function.
Therefore, your answer of (0,10) is not correct, as (0,10) is not within the feasible region.