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 15 minutes of finishing and inspection time.

1) Write the LP Formula

2) Solve the solution with solver in excel.

Answer 1

Variable

Deluxe model number = D, Special Model number = S

Constraints

1. D and S are non-negative integers

2. total construction hours = 20D + 15S <= 100

3. total inspection hours = 10D + 15S <= 80

Objective

Maximize profit = 12D + 10S

Solution

		per model			Total
Model	optimial number	Construction	inspection	Profit	Construction	inspection	Profit
Deluxe	2	20	10	12	40	20	24
Special	4	15	15	10	60	60	40
Total					100	80	64
Max possible					100	80
Constraint					0	0

so 2 deluxe and 4 special models.