Question

Brenda wants to buy a new car and has a budget of $50,000.

She has just found a magazine that assigns each car an index for styling and an index for gas mileage. Each index runs from 1 to 10, with 10 representing either the most styling or best gas mileage. While looking at the list of cars, Brenda observes that on average, as the style index increases by one unit, the price of the car increases by $12,500.

She also observed that as the gas-mileage index rises by one unit, the price of the car increases by $10,000.

Illustrate the various combinations of style (S) and gas mileage (G) that Brenda could select with her

$50,000 budget.

Answer 1

We have the following information about Brenda

• Budget = $50,000

• As the style index increases by one unit, the price of the car increases by $12,500.

• As the gas-mileage index rises by one unit, the price of the car increases by $10,000.

Now If she considers styling, she has a budget of 50000 so the most styling she can have is of 50000/12500 = 4 units. Similarly, under the gas-mileage index the most  she can get is a car with a gas-mileage of 50000/10000 = 5 units.

The various components now lie between these two coordinates and the line that joins them (0, 4) and (5, 0) where gas-mileage index units are measured on x-axis

.