what point in the feasible region maximizes the objective function
x>0
y>0
constraints -x+3+y
y,1/3x+1
Object function C+5x_4y
To find the point in the feasible region that maximizes the objective function, we need to follow these steps:
1. Plot the feasible region: The given inequalities define the constraints. Start by plotting the lines x = 0 and y = 0, which represent the non-negativity constraints x > 0 and y > 0, respectively. Then, plot the lines -x + 3 + y = 0 and y = 1/3x + 1. Shade the region that satisfies all the constraints.
2. Find the corner points of the feasible region: Identify the points where the lines intersect in the shaded region. These intersection points are the corner points of the feasible region.
3. Evaluate the objective function at each corner point: Once you have identified the corner points, substitute the x and y values of each corner point into the objective function C + 5x + 4y. Calculate the resulting value for each corner point.
4. Determine the maximum value: Identify the point that gives the maximum value when substituted into the objective function. This will be the point in the feasible region that maximizes the objective function.
Note: The objective function you provided, C + 5x_4y, seems to have a typo. Please clarify or correct the objective function to get the correct maximum value.