Apex and Zenith are two tech corporations competing in a deterministic patent race for a new generation of electric batteries. The required time T (in years) in order to complete the necessary R&D and to apply for the patent is a function of the funds R (in millions) used for this research project and it is given by the function below: T = 160 - 10R The company that wins the patent is expected to earn a profit of 100 million from its commercial exploitation. Apex has 50 million of available funds in terms of cash and bank loans, which it can use to fund the project, while Zenith has 30 million of available funds. a. If Apex invests 10 million in the project, how much do you expect Zenith to invest and why? (5 points) b. If both companies invest in the project at the same time, which company do you expect to win the patent race and why? (10 points) c. Provide the set of all possible outcomes in this patent race which survive profitable deviation from one of the two companies. (15 points)