You are managing a vending machine which generates an average daily profit of $2000 when it is working, but it breaks down each day independently with probability q = 0.2. A repair company offers a service contract to restore the machine to working order with probability p in one day whenever it to breaks down, at a cost of $ 100/1-p each day (whether the machine is working or not). You get to choose p. What value of p should you choose to maximize your expected profit? (Please found exact values)