You are involved in new model development at a major automobile company. The company is planning to introduce two new plug-in hybrid electric vehicles: the subcompact Green Town Hopper and the midsize Electra Supreme, and your department must decide on the degree of hybridization (DOH) for each of these models that will result in the largest reduction in gasoline consumption. (The DOH of a vehicle is defined as the ratio of electric motor power to the total power; it typically ranges from to . For example, a model with a DOH has an electric motor that delivers of the total power of the vehicle.)

The tables below show the benefit for each of the two models, measured as the estimated reduction in annual gasoline consumption, as well as an estimate of retail cost increment, for various DOH percentages. (The retail cost increment estimate is given by the formula for the Green Town Hopper and for the Electra Supreme.)

1. Repeat the computations above for the Earth Suburban using the following data:

   Earth Suburban

   DOH (%)	10	20	50
   Reduction in Annual Consumption (gals)	240	330	300
   Retail Cost Increment ($)	9,000	9,500	11,000

2. Repeat the analysis for the Green Town Hopper, but this time take to be the cost increment, in thousands of dollars. (The curve of benefit versus cost is referred to as a cost-benefit curve.) What value of DOH corresponds to the optimal cost? What do you notice? Comment on the answer.

3. Repeat the analysis for the Electra Supreme, but this time use the optimal values, , gallons per year in place of the data. What do you notice?

4. Find the equation of the parabola that passes through the points , , and .

5. Is there a parabola that passes through the points , , and ?

6. Is there a parabola that passes though the points , , , and ?

7. You submit your recommendations to your manager, and she tells you, Thank you very much, but we have additional data for the Green Town Hopper: A DOH results in a saving of gallons per year. Please resubmit your recommendations taking this into account by tomorrow. [Hint: You now have four data points on each graph, so try a general cubic instead: . Use a graph to estimate the optimal DOH.]