Question

Maximize p = 2x 3y 1.1z 4w subject to 1.2x y z w ≤ 81 2.2x y − z − w ≥ 20 1.2x y z 1.2w ≥ 21 x ≥ 0, y ≥ 0, z ≥ 0, w ≥ 0.

A) Maximize
B) Optimize
C) Solve
D) Determine

Answer 1

Maximize p = 2x 3y 1.1z 4w subject to constraints using the simplex method.

Step-by-step explanation:

The given problem is a linear programming problem, so the correct option in this case is A) Maximize. To solve this problem, we can use the simplex method. Here are the steps:

1. Convert the inequalities into equations by adding slack variables: 1.2x + y + z + w + s1 = 81, -2.2x - y + z - w + s2 = -20, -1.2x - y - z - 1.2w + s3 = -21.
2. Create the initial simplex tableau by putting all the coefficients and variables in a matrix.
3. Choose the pivot column by selecting the most negative coefficient in the objective row.
4. Choose the pivot element by selecting the smallest nonnegative constant value in the pivot column.
5. Perform row operations to turn the pivot element into 1 and make the other elements in the pivot column 0.
6. Repeat steps 3-5 until there are no negative coefficients in the objective row.

The optimal solution will be the values of x, y, z, and w that maximize the objective function p = 2x + 3y + 1.1z + 4w.