Q1) "Investment" (zero cost) has 80% chance of paying $125 and a 20% chance of losing $375. I understand that expected payout is (.8x$125)-(.2x$375)=$25. I can make this "investment" every month. Or we can say, how much money do I need to have say 98% probability of not going broke and being able to reap expected long them expected pay-off of the $25/month".
Revenue and cost functions for producing and selling quantity x for certain production facility are given below.
R(x) = 12x - x2
C(x) = 18 + 3x
a) Find out profit function P(x).
b) Use Excel to sketch functions R(x), C(x) and P(x) for the interval 0≤ x ≤ 10. Copy and paste graph below. Use Scatter plot with smooth lines and markers.
c) Calculate the break-even quantities.
d) Find out the marginal revenue R'(x).
e) Find out the marginal cost C'(x)
f) At what quantity is profit maximized?