Consider the decision problem given below. Construct a decision diagram of the problem. You do not need to model the decision tree or recommend an alternative.

You are considering two design options for a car seat. The first option has a strong heritage on previous developments $($heritage seat$),$ guaranteeing a really good performance during the car crash test, but its customer appeal is not great. The second option, based on some innovative materials that your company has developed $($novel seat$)$ has the potential of being very appealing to the customers. However, there are some doubts about its performance at the car crash test.

The total production cost of the heritage seat is estimated at $$25$M$,$ will take $10$ months to produce, and you expect to obtain a revenue of $$100$M$.$ The total product cost of the novel seat is estimated at $$55$M$,$ may take $12$ months $($at $25\%$ confidence$)$ or $18$ months $($at $75\%$ confidence$)$ to produce, and you expect to obtain a revenue of $$100$M$,$ $$150$M or $$200,$ depending on market performance of the car. Both designs meet your delivery needs, so there is no expectation of any penalty due to schedule and your customer $($the car manufacturer$)$ has not established any financial incentive for early deliveries. Your business development expert estimates those revenue levels at $20\%,50\%,$ and $30\%$ confidence. This is assuming that the car crash test is successful, which you believe will be at $50\%$ confidence. If the seat fails during the car crash test, you will face a $$20$M penalty and, in addition, you may lose the contract, although your business development expert estimates that there is a $65\%$ chance that the car manufacturer will still buy the heritage seat from you in that case, although at $85\%$ its current price.

The engineers in your team suggest performing additional mechanical testing on the novel seat before committing to one of the designs. The test will cost $$2$M and it will imply a delay of $2$ months, for which the car manufacturer will apply to you a $$10$M penalty, but it may be worth considering. The test is a good predictor for the performance of the seat during the car crash test. Specifically, the test successfully predicts $90\%$ of the successful car crash tests and $80\%$ of the unsuccessful car crash tests.

Another team of engineers suggest adding an underlying coating of another material, which would improve the workmanship during production. They believe that the overall strength would increase by $30\%$ and only increase production cost by $5\%.$ Mechanical engineers estimate that the increased strength will have no effect on the performance of the seat during car crash testing and business development indicates that it will not lead to any increase in revenue either.

You are an engineering manager with a strong reputation for on$-$time deliveries; you have never delivered late and want to maintain a clean record. As an established car seat manufacturer in the market, though, your company has set the objective for your project to maximize profit. Provide a recommendation of how to proceed.