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 least 40 percent of the production total. (a) Formulate the above problem as a linear programming problem. (b) Find the solution graphically that gives the maximum profit.
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 least 40 percent of the production total. (a) Formulate the above problem as a linear programming problem. (b) Find the solution graphically that gives the maximum profit.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Need A and b with graph pls
Transcribed Image Text: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 least 40 percent of the production total.
(a) Formulate the above problem as a linear
programming problem.
(b) Find the solution graphically that gives the maximum
profit.
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