Question

Given constraints: x≥0, y≥0, 2x+2y≤4, x+y≤8. Explain the steps for maximizing the objective function P=3x+4y.

a. Identify feasible region
b. Plot constraints on a graph
c. Find corner points of feasible region
d. Substitute corner points into the objective function

Answer 1

To maximize the objective function P=3x+4y given the constraints, you need to identify the feasible region, plot the constraints on a graph, find the corner points of the feasible region, and substitute these points into the objective function.

Step-by-step explanation:

Steps for maximizing the objective function P=3x+4y:

1. Identify feasible region: The feasible region is the set of all points that satisfy the given constraints. In this case, the feasible region is the intersection of the non-negative quadrant (x≥0 and y≥0) and the region defined by the inequalities 2x+2y≤4 and x+y≤8.
2. Plot constraints on a graph: Plot the lines representing the equations 2x+2y=4 and x+y=8 on a graph. Shade the region that satisfies the inequalities.
3. Find corner points of feasible region: The corner points of the feasible region are the vertices of the shaded region. Find the points where the lines intersect or touch the axes.
4. Substitute corner points into the objective function: Substitute the x and y values of each corner point into the objective function P=3x+4y and calculate the corresponding values of P.