# R&D Costs

• Mar 16th 2011, 11:13 AM
ikebukuro
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?
• Mar 16th 2011, 08:53 PM
dwsmith
Quote:

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 $E[C]$ function and set it equal to zero.
• Mar 16th 2011, 11:32 PM
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.
• Mar 17th 2011, 01:27 PM
dwsmith
Quote:

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.