Final answer:
To solve the given linear program, graph the constraints in the first quadrant and identify the feasible region. Determine the vertex solutions by finding the intersection points of the constraints, then evaluate the objective function at these corner points to find the maximum value.
Step-by-step explanation:
To solve the linear program, we need to first identify the feasible region determined by the constraints given. We'll graph the equations as follows:
- -x1 + x2 ≤ 5
- x1 - x2 ≤ 0
- x1 ≤ 5
- x1 ≥ 0
- x2 ≥ 0
Since x1 and x2 are both greater than or equal to 0, we are limited to the first quadrant of the coordinate plane. Draw each line with the corresponding inequality and fill the region that satisfies all constraints. The intersection of these areas will be the feasible region.
The corner points of the feasible region, also known as vertex solutions, can be found by considering the intersection points of the boundaries of the feasible region. These points are important as the solution to a linear programming problem lies at one of the corner points.
One way to find the corner points is to solve the system of linear equations that we get when we take the equalities corresponding to each of the inequalities. For example, to find the intersection of -x1 + x2 = 5 and x1 = 5, we substitute x1 = 5 into the first equation, yielding points. We repeat this process for all combinations of constraints to find all corner points.
After finding the corner points, we can evaluate the objective function, Z = x1 + x2, at each corner point to determine the maximum value. This process allows us to identify the optimal solution to the linear programming problem.