Individuals gain utility from vehicle miles traveled, v, vehicle safety, S, and some other good, x. Assume further that automobile safety is a decreasing function of fuel efficiency (miles per gallon, MPG). This is plausible as, ceteris paribus, making a car safer often requires the designer to add extra weight, reducing the fuel efficiency. Assume that consumers can choose the level of fuel efficiency they want for their car. The price of fuel is p_g and the price of x is p_x. For the purposes of this problem, assume that there are no costs other than fuel costs associated with owning and operating the vehicle. Set up the individual’s utility maximization problem and derive the system of equations that describes the individual’s optimal choice of v, MPG, and x.