Oakton Manufacturing makes two types of rocking chairs specifically designed for men and women known as the His and Hers models. Each chair requires four legs and two rockers but differing numbers of wooden dowels. Each His chair requires four short dowels and eight long dowels while each Hers chair requires eight short dowels and four long dowels. Each His chair contributes $10 in profit while each Hers chair contributes $12. The company has 900 legs, 400 rockers, 1200 short dowels, and 1056 long dowels available. The company wants to maximize its profit while also ensuring that it makes at least half as many His chairs as Hers chairs.

Required:
a. Formulate an LP model for this problem.
b. Sketch the feasible region for this problem.
c. Find the optimal solution.

Question

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Respuesta :

jtellezd jtellezd · Answer 1 · 2021-06-22T03:58:06+02:00

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 $