A startup has just finished developing a new product and they are about to launch. The Data Science team, using historical data has concluded that there are two cases: either the market will respond well to the product in which case the daily demand is given by DH(p)=300-2p or the market will not respond well to the product in which case the daily demand will be given by DL(p)=100-p.
a) What is the optimal price and revenue when the market responds well to the product?
b) What is the optimal price and revenue when the market does not respond well to the product?
c) You are a venture capitalist and you estimate that the probability that the market will respond well is probability 0.7. You are given the option to invest in the company before the launch of the product. How much would you be willing to invest in exchange of 10% of the revenues? You can assume that you expect the startup to be operating for two years.