question 1

QUESTION 1 [10] 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. What mix of products should be produced and what is the maximum profit? Required: Use the graphical method to illustrate and the corner-point method to find the optimal solution. Show the profits for each corner point. Show the feasible area and corner points on graph. Note: Let x1 = number of Deluxe models produced and X2 = number of Special models produced