please show your mathematical solution . that part i can use.

(30p) A pharmaceutical company is developing a new vaccne. If company markets the vaccine and it is successful, it will earn a $40,000 profit; if it fails, the company will lose $25,000. In the past, the success rate of similar products has been around 45%. An R\&D study on effectiveness can be carried out at an additional cost of $4,000. If the study result is favorable, there is an 85% chance that the vaccine will be successful. If not, there is only a 20% chance that the product succeeds in the market. The management believes that study will yield a favorable result with 55% possibility. Determine company's optimal strategy by building a decision tree and find the expected value of sample information (EVSI) as well as expected value of perfect information (EVPI)