Answer:
x = 76 y = 112 z (max) = 2104 $
Step-by-step explanation:
legs rockers short dowels long dowels Profit $
Model His (x) 4 2 4 8 10
Model Her (y) 4 2 8 4 12
Availability 900 400 1200 1056
From the table above we find z
Objective Function z :
z = 10*x + 12*y to maximize
Subject to
Constraint 1 quantity of legs available: 900
4*x +4*y ≤ 900
Constraint 2 quantity of rockers available: 400
2*x + 2*y ≤ 400
Constraint 3 quantity of short dowels available: 1200
4*x 8*y ≤ 1200
Constraint 4 quantity of long dowels available: 1056
8*x + 4*y ≤ 1056
Constraint 5 condition between x and y
x ≥ 0.5*y
The model:
z = 10*x + 12*y to maximize
Subject to:
4*x +4*y ≤ 900
2*x + 2*y ≤ 400
4*x 8*y ≤ 1200
8*x + 4*y ≤ 1056
x ≥ 0.5*y or x - 0.5*y ≥ 0
General constraints:
x ≥ 0 y ≥ 0 both integers
After 6 iterations with AtomZmath on-line solver optimal solution is:
x = ��76 y = 112 z (max) = 2104 $
