You are the Chief Data Analytic Officer of a large pharmaceutical company. Your company currently has two drugs A and B under development for treading two different diseases, with 79% and 80% efficacy (chance of curing a patient) respectively on each patient based on your clinical research so far. To get approval from FDA, you need to show effectiveness on at least 800 out of the 1,000 patents tested in the final clinical trial. You cannot market a drug with

the FDA approval.

Hint: You can model the FDA approval process using a Binomial distribution with n=1000 and p = 0.79 (for A, 0.80 for B).

Your team has collected the following information on these two drugs. Please note, if your product does not pass the FDA test, you wont be able to market the product so you wont have sales, nor marketing promotion expenses; but you do incur R&D expenses.

	Drug A	Drug B
R&D budget (x ) ($ million)	3	6
Efficacy rate ( R )	79%	80%
Marketing promotion budget (y ) ($ million)	7	9
Market size (# of patients in million)	35	30
Market share (S ) mean*	8%	10%
Market share - standard deviation	2%	3%
Drug price per patient ($)	12	10

* Market share achieved is uncertain but can be described by a normal distribution with the given mean and standard deviation. The market share given in the table above will be reduced if there is a competitor in the market. The reduction is 20% on average but it is distributed uniformly between 18% and 22%. Your team estimates that there is a 70% chance that your company will have a competitor in each of the two markets. Presence of competitor in one market does not affect the other market, i.e., they are independent random events.

3.1. Simulation (6 points)

3.1.1 Build a Monte Carlo simulation model to estimate the total profit that your company can be expected to achieve for the two drugs. Label this worksheet as Problem 3.1 (4 points)

3.1.2 What is the total expected profit (or loss)? (1 point)

3.1.3 What is the probability that your company will be profitable? (1 point)

3.2. Stochastic Optimization (6 points)

Now assume that the drug efficacy rate (R ) can be influenced by R&D spending (x , stated in million dollars) with the following relationship

R=1-e- ax

where a is a parameter between 0 and 1.

3.2.1. Find out the parameters a in the above function for each of the products so that R= 0.79 for Product A and R= 0.80 for Product B (1 point).

a = _______________ for Product A

a = _______________ for Product B

3.2.2 On a separate worksheet labeled as Problem 3.2, setup a stochastic optimization model to find the allocation of the R&D budget among the two products that achieves the maximum expected total profit. The $9 million total R&D budget needs to be satisfied only 90% of the time (2 points)

3.2.3 What is optimal allocation of the R&D budget of the $9 M to each of the product and what is the expected total profit? (1 point)

Hint: Try multiple initial solutions to get the best result that you can.

3.2.4 What is the probability that your company will make a profit in this case? (1 point)

3.2.5 If you are able to raise an extra $1M for R&D spending, what would you do in your R&D investment decision and what profit that you would expect to get? (1 point)

Hint: Again, try multiple initial solutions to get the best result that you can.