Question

Maximize p=3x1 4x2−5x3, subject to: 2x1−3x2 2x3 ≤4 x1 2x2 4x3 ≤8 x2−x3 ≤6 x1,x2,x3 ≥0 and give the maximum value of p to the nearest integer.

Answer 1

To maximize the function p=3x1 + 4x2 - 5x3 with given constraints, one must solve a linear programming problem, find the values of x1, x2, x3 that maximize p, and then calculate the maximum p value, rounding it to the nearest integer.

Step-by-step explanation:

To maximize the objective function p=3x1 + 4x2 - 5x3, we need to consider the constraints given by the inequalities: 2x1 - 3x2 + 2x3 ≤ 4, x1 + 2x2 + 4x3 ≤ 8, x2 - x3 ≤ 6, and x1, x2, x3 ≥0. The problem is to find the values of x1, x2, and x3 that give the maximum value for p while satisfying the constraints. This is a typical linear programming problem which can be solved using the simplex method, graphic method, or by using optimization software.

After solving, you will get the values of x1, x2, and x3 that maximize p. You should then plug these values into the objective function to get the maximum value of p. The value of p obtained from the solution should be rounded to the nearest integer to provide the final answer.