You won the lottery and are now able to invest in your biggest dream-a Tesla Model S, P100D. Tesla just found a way to sell back the stored electricity to the grid at the same cost as charging. However, each workday you have a busy travelling salesman schedule, meaning that you have only one hour at work to charge/discharge your car before you drive 200 km to your home, corresponding to a need of 48 kWh. Now you want to figure out how to charge or discharge KW Parameter Value Min. storage/your demand kWh 48 Max storage kW 100 Max. charge to car kw 11 Max. discharge to grid 11 Initial storage level kWh Storage value /kWh 0.025 Cost of charging/profit of discharging /kWh 0.015 Table 1: Data for the Tesla car your car in the hour before going home in order to earn the most money and still being able to return home in your car. Remember that the storage level also has a value as you might sell the electricity later. Assume that the there are no transmission losses, i.e. charge/discharge has an efficiency of 100% Let XI denote the storage level, and x2 denote the charge and discharge of the battery such that if x2 > 0 the car is charging and if x2 0 the car is charging and if x2