how to do this question

Problem 4. (16 points) There are 3 key stages of trials that need to be completed in order to produce a vaccine. However, each stage may fail and the probability of successfully complete the trial of that stage is higher when there are more workers involved. The following table shows the probabilities: Probability of success number of workers | Stage 1 Stage 2 Stage 3 1 05 0.6 0.7 2 0.6 0.7 0.8 3 08 0.9 1 Accordingly, hiring more workers incurs higher cost and the cost is different for each stage. The cost is shown below. For example, hiring 2 workers for stage 2 costs 4000 dollars and hiring 3 workers for stage 1 costs 3000 dollars. _ total cost number of workers | Stage 1 Stage 2 Stage 3 1 L1000 2000 1000 2 2000 4000 3000 3 3000 5000 4000 A maximum amount of 7000 dollars can be expended on this vaccine. Use dynamic pro- gramming to find out the optimal policy to maximize the probability of successfully deliver the vaccine. Note that the vaccine can be delivered only if all the 3 stages trials succeed. For example, if stage 2 fails, no matter how much budget remains and how many workers vou hire in stage 3, the probability of successfully deliver the vaccine is 0