Model formulation:
Decision variables: Let x grams of ingredient A and y grams of ingredient B be used.
The objective function is: Minimize z = 80x + 50y
Subject to the constraints: 3x + y ≥ 6
(Antibiotic 1 constraint) x + y ≥ 4
(Antibiotic2 constraint) 2x + 6y ≥ 12
(Antibiotic 3 constraint) x ≥ 0 and y ≥ 0
Solution:
We see that the minimum value of z is $230 and occurs when x = 1 and y = 3
The optimum solution is ingredient A = 1 gram and ingredient B = 3 grams.
The minimum cost is $230.