The given primal problem is:
Max Z = 3𝑥1 + 4𝑥2 + 7𝑥3
Subject to:
𝑥1 + 𝑥2 + 𝑥3 ≤ 10
4𝑥1 − 𝑥2 + 𝑥3 ≥ 15
𝑥1 + 𝑥2 + 𝑥3 = 7
𝑥1, 𝑥2 ≥ 0, 𝑥3 unrestricted
To form the dual of the given primal problem, we first need to assign the dual variables to each constraint in the primal problem:
Let the dual variables be y1, y2, and y3 corresponding to the first, second, and third primal constraints, respectively.
The dual of the given primal problem is:
Min W = 10y1 + 15y2 + 7y3
Subject to:
y1 + 4y2 + y3 ≥ 3
y1 - y2 + y3 ≥ 4
y1 + y2 = 7
y1, y2, y3 ≥ 0
Therefore, the dual problem is a minimization problem with the given constraints.
Question B1. Form the Dual of the following Primal. (4 Marks)
Max Z = 3𝑥1 + 4𝑥2 + 7𝑥3
Subjected to
𝑥1 + 𝑥2 + 𝑥3 ≤ 10
4𝑥1 − 𝑥2 + 𝑥3 ≥ 15
𝑥1 + 𝑥2 + 𝑥3 = 7
𝑥1, 𝑥2 ≫ 0, 𝑥3 → 𝑢𝑛𝑟𝑒𝑠𝑡𝑟𝑖𝑐𝑡𝑒𝑑.
1 answer