Solution
The correct answer is Option 1
EXPLANATION:
| |
Vitamin D |
Vitamin E |
Cost |
| x |
6 |
7 |
12 |
| y |
8 |
12 |
20 |
| Min Z |
100 |
120 |
|
The dual of a Linear Programming Problem (LPP) interchanges the role of the objective function coefficients and right-hand side constants from the primal problem. They also interchange the constraint coefficients matrix and relations.
In the primal problem, we're minimizing cost subject to constraints that ensure we have enough vitamins. In the dual, we'd be maximizing vitamin intake with cost constraints.
So, from the primal problem's constraints: 6x + 8y ≥ 100 (for Vitamin D) becomes 6u + 8v ≤ 12 (for the cost of Food X), and 7x + 12y ≥ 120 (for Vitamin E) becomes 7u + 12v ≤ 20 (for the cost of Food Y).
The objective changes as well, the minimization of cost becomes maximization of vitamins. So 'Min Z = 12x + 20y' changes to 'Max Z = 100u + 120v'.
So, the correct dual for the LP problem is:
Max Z = 100u + 120v
s.t 6u + 7v ≤ 12 8u + 12v ≤ 20 u, v ≥ 0