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. The company has also decided that the Special model must comprise at most 60 percent of the production total.

please explain the 60 % part NO EXCEL MUST BE DONE BY HAND

Answer 1

Let me consider that,   x = Number of Deluxe models to be produced, y = number of Special models to be produced, According to the given Data, The profit per unit on the Deluxe model is $12, while the profit per unit on the Special model is $10 So, Objective function is   Maximize 12x + 10y,(Maximize the profit) As, The Deluxe model requires 20 minutes of Construction time, the Deluxe model requires 10 minutes of Finishing and Inspection time. As, The Special model requires 15 minutes of Construction time, the Special model requires 15 minutes of Finishing and Inspection time. There are only 100 hours available daily at the construction stage and only 80 hours available at the finishing and inspection stage. Thus, Constraints are    subject to 20x + 15y ≤100*60 or 6000 10x + 15y ≤80*60 or 4800 The company has also decided that the Special model must comprise at most 60 percent of the total production As Total Production would be x + y, again, Special Model would be maximum 60% of the total quantity(x + y), So, y ≤ 0.6(x + y), Or, 0.4y – 0.6x≤0 Or, 4y – 6x ≤ 0, X >= 0 and y >= 0 Using, Graphical Method, we get, Thus, Objective function is   Maximize 12x + 10y,(Maximize the profit) = 3811.764706 Maximum = 3812 Rounded Number of Deluxe models to be produced = 141.176471 = 141 Rounded number of Special models to be produced = 211.764706 = 212 Rounded

Graph for above data,