A) Linear Programming is used in all types of organizations in order to solve a wide variety of problems. Understanding the types of problems, and how LP problems can be modeled in Excel, and how optimal solutions can be found using Excel’s Solver add-in, are powerful methods of quantitative analysis. Typically, most of our efforts go into the development of the model. Develop a model for the following scenario which maximizes company profit and display this graphically. Use SolverTable to monitor the decision variables and the total profit.
Problem:
An electric vehicle company manufactures electric cars and SUVs. The amount of nickel used per vehicle is a strong contributor toward the development of electric vehicles and is being taken into effect as the main contributor used to maximize profit. Other materials are involved but this problem will focus on nickel alone.
Each electric SUV uses 40 ounces of nickel and produces $4,000 profit. Each electric car uses 30 ounces of nickel and produces $2,500 in profit. Marketing restrictions require that the number of cars produced must be at least twice the number of SUVs produced. There is 20,000 ounces of nickel available. A conversion of ounces to pounds can be performed in the tabulated results if necessary.
40 ounces = 2.5 pounds
30 ounces = 1.875 pounds.
20,000 ounces = 1,250 pounds
- Maximize the company’s profit using Solver.
- Represent the data visually in order to show the maximized company profit.
- Use SolverTable to show what happens to the decision variables and the total profit when the availability of nickel varies from 10,000 to 30,000 in 1,000 ounce increments. How many extra ounces of nickel would the company be willing to pay for over its current 20,000 ounces? How much profit would the company lose if it lost any of its current 20,000 ounces?
B) In any optimization model such as those in this chapter, we say that the model is unbounded (and Solver will indicate as such) if there is no limit to the value of the objective. For example, if the objective is profit, then for any dollar value, no matter how large, a feasible solution exists with a profit at least this large. In the real world, why are there never any unbounded models? If you run Solver on a model and get an “unbounded” message, what should you do?
Using a graphic organizer of your choice, create a visual graphic that explains your answers to the questions above. Then, post your graphic organizer as an attachment. Use your creativity to make it appealing and clear enough for your classmates to understand, and reflect and comment upon.
