Answer:
z (min) = 105
x₁ = 3
x₂ = 2
Step-by-step explanation:
Let´s call x₁ (number of tables) and x₂ ( number of capsules)
assuming it is only possible to get a whole table or capsule we have:
Table x₁ 8 u myra X 1 u of myra Y and 2 u of myra Z
Capsule x₂ 2 " 1 " and 7 u "
Objective function
z = 15* x₁ + 30* x₂ to minimize
First constraint ( Myra X )
8*x₁ + 2*x₂ ≥ 16
Second constraint ( Myra Y )
x₁ + x₂ ≥ 5
Third constraint ( Myra Z )
2*x₁ + 7*x₂ ≥ 20
General constraints x₁ ≥ 0 x₂ ≥ 0 both integers
Then the model is:
z = 15 * x₁ + 30 * x₂ to minimize
Subject to
8*x₁ + 2*x₂ ≥ 16
x₁ + x₂ ≥ 5
2*x₁ + 7*x₂ ≥ 20
x₁ ≥ 0 x₂ ≥ 0 both integers
As the constraints, all are of the form ≥ we have to subtract surplus variables sₐ and add artificial variables Aₐ
sₐ ≥ 0 Aₐ ≥ 0
The first table is
z x₁ x₂ s₁ s₂ s₃ A₁ A₂ A₃ = Cte
1 - 15 - 30 0 0 0 M M M = 16
0 8 2 -1 0 0 1 0 0 = 5
0 1 1 0 -1 0 0 1 0 = 20
0 2 7 0 0 -1 0 0 1 = 20
Using AtoZmax and after 6 iterations we find
z (min) = 105
x₁ = 3
x₂ = 2
