As a supervisor of a production department, you must decide the daily production

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 least 40 percent of the 1. production total a. Create a linear programming model using Excel and Data Solver b. Find the solution that gives the maximum profit Instructions: Model must follow the example of the homework problems and inchude the following 1. Include the Maximie Equation 2. Inchude all Variables 3. Include all constraints 4. Inchude signs (inequality) for all constraints 5. Include a screen shot of the solver dialog box after you have it filled out 6. Inchude the objective (Profit or costs 7. Must be submitted in Excel version with all proper labels and formulas

Explanation / Answer

Let D be deluxe model

and S be special model

Maximize Z=12D+10S

subject to the following constraints:

20d+15S<=100

10D+15S<=80

Non-Negativity Constraints x>=0,y>=0

Test points using points of intersection gives (2,4)

12D+10S=z=12*2+10*4=64

(5,0)

12D+10S=z=60

(0,5.333)

12D+10S=z=53

64 is the greatest profit out of three points

So (2,4) two deluxe and 4 special is maximum profit

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