# Thread: R&D Costs

1. ## R&D Costs

A pharmaceutical firm can develop a patentable face cream using either of two independent processes, each of which has a 25 percent chance of costing $5 million, a 25 percent chance of costing$10 million, and a 50 percent chance of costing $20 million. If the firm can determine the true cost of both processes after spending$2 million on each, what is the minimized expected cost of developing the patent?

Solution: 12.313

Any ideas HOW to arrive at 12.313?

2. Originally Posted by ikebukuro
A pharmaceutical firm can develop a patentable face cream using either of two independent processes, each of which has a 25 percent chance of costing $5 million, a 25 percent chance of costing$10 million, and a 50 percent chance of costing $20 million. If the firm can determine the true cost of both processes after spending$2 million on each, what is the minimized expected cost of developing the patent?

Solution: 12.313

Any ideas HOW to arrive at 12.313?
Since it says mimize, you need to take the derivative of the $\displaystyle E[C]$ function and set it equal to zero.

3. Well, there's no explicit cost function here. Even if I go for the C(index) derivatives, the only thing left will be probabilities, which altogether add up to 1.

4. Originally Posted by ikebukuro
Well, there's no explicit cost function here. Even if I go for the C(index) derivatives, the only thing left will be probabilities, which altogether add up to 1.
You need to determine the expect cost.