Question

(20 pts.) 2. As a supervisor of a production department, you s 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 per unit. Each model goes through two phases in the production process, and there are only 100 man- hours available daily at the construction stage and only 80 man-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 15 minutes of finishing and inspection time. The company has also decided that the special model must comprise at least 40 percent of the production total. Formulate this problem as a linear programming problem. Clearly define your decision variables and identify what each constraint refers to.

Answer 1

Let assume D represent the Deluxe and S represent S.

Decision Variable -

To find out the value of D and S to maximize the profit.

Objective Function -

Max Z = 12D + 10S

Constraints -

Construction stage - 20D+15S <=100*60

20D + 15S <= 6000

Finishing and Inspection stage - 10D + 15S <= 80*60

10D +15S <= 4800

Production Quantity - S >= 0.40*(D+S)

Integer Constraints - S,D = integer