Question

What is the objective of the linear programming problem with the following constraints:

Maximize 1x1 + 1x2
Subject to:
4x1 + 7x2 ≤ 31
1x1 + 5x2 ≤ 15
2x1 + 1x2 ≤ 13
x1, x2 ≥ 0 (both must be integers).

Answer 1

The objective of a linear programming problem is to maximize or minimize a linear function called the objective function, subject to a set of constraints.

Step-by-step explanation:

The objective of a linear programming problem is to maximize or minimize a linear function called the objective function, subject to a set of constraints. In this case, the objective is to maximize the function 1x1 + 1x2. The constraints are:

• 4x1 + 7x2 ≤ 31
• 11x1 + 5x2 ≤ 15
• 2x1 + 1x2 ≤ 13
• x1 and x2 must be greater than or equal to 0 and both must be integers.

To solve this problem, you can use a method called the simplex algorithm or graphing to find the values of x1 and x2 that maximize the objective function while satisfying the constraints.