Question

As a supervisor of a production department, you must decide the daily production totals of a certain product that has two models, the Deluxe and the Special. The profit on the Deluxe model is $12 per unit and the Special's profit is $10. Each model goes through two phases in the production process, and there are only 100 hours available daily at the construction stage and only 80 hours available at the finishing and inspection stage. Each Deluxe model requires 20 minutes of construction time and 10 minutes of finishing and inspection time. Each Special model requires 15 minutes of construction time and 25 minutes of finishing and inspection time. The company has also decided that there must be at least 150 Special models produced. Write the LP formulation to determine the optimal production mix of Deluxe and Special models.

Answer 1

Answer: Let's summarize the given problem as mentioned in the below table:

(Note: We have converted the time from minutes to an hour by dividing the value by 60)

Decision Variable:

Let, X = No. of Deluxe models produced, and Y = No. of Special models produced

Objective Function:

Here, the objective is to maximize the total value. So, the objective function =

MaxZ = 12X1 + 10X2

Subject to Constraints:

C1 = 0.33X1 + 0.25X2 < 100 (Time Constraint at Construction Stage)

C2 = 0.17X1 + 0.42X2 < 80 (Time Constraint at Finishing and Inspection Stage)

C3 = X2 > 150 (Volume Constraint for Special Model)

Non-Negativity Condition:

X1, and X2 > 0

(Note: As the last line of the question suggests, we have just formulated the LP problem and not solved it)