Question

Objective: Min= P1+P2+P3+P4+P5+P6.

Constraints:
P1+P2 >12
P2+P3 > 16
P3+P4 >9
P4+P5 >11
P5+P6 >4
P6+P1> 3
Solve for Min

Answer 1

To solve for the minimum value of the objective function with the given constraints, we can use a technique called linear programming. Here's how: Assign variables to each of the unknowns. Write the system of constraints as inequalities. Set up the objective function as the sum of all the variables.

Step-by-step explanation:

To solve for the minimum value of the objective function with the given constraints, we can use a technique called linear programming. Here's how:

1. Assign variables to each of the unknowns, such as P1, P2, P3, P4, P5, and P6.
2. Write the system of constraints as inequalities:
3. P1 + P2 > 12
4. P2 + P3 > 16
5. P3 + P4 > 9
6. P4 + P5 > 11
7. P5 + P6 > 4
8. P6 + P1 > 3
9. Set up the objective function as the sum of all the variables:
10. Min = P1 + P2 + P3 + P4 + P5 + P6
11. Graph the system of inequalities to find the feasible region.
12. Find the vertices of the feasible region.
13. Substitute the values of the vertices into the objective function.
14. Compare the results to find the minimum value.