Steve Young, a Senior Sales Development Representative at a local wellness gift shop, is

preparing for the upcoming Chinese New Year $($CNY$)$ Sales. He is considering two new CNY

gift products: "Healthy Treats" and "Forever Youth". While there is some overlap in their

targeted customer groups, they are not complete substitutes for each other.

With only one month remaining to make his purchasing decision, Steve faces a time constraint

due to the long lead time required for production and shipping to Singapore. Once a decision

is made, he cannot alter the purchase quantity. Additionally, Steve is required to order both

types of products; he cannot opt to order just one of them.

Steve needs to determine the specific purchasing quantity for each product within this month.

The options are either $200$ units, indicating a low demand estimation, or $500$ units, indicating

a high demand estimation. The unit purchasing cost for Healthy Treats is $$50,$ and for Forever

Youth, it's $$75.$ The market prices are fixed at $$120$ for Healthy Treats and $$180$ for Forever

Youth. If any products remain unsold during the CNY sales, the disposal costs are $$10$ for

Healthy Treats and $$15$ for Forever Youth.

Based on a combination of experience and current trend analysis, Steve estimates a $30\%$ chance

that the demand for Healthy Treats will be high, exceeding $500$ units.

Before finalizing his purchasing decision, Steve has the option to conduct a regional market

research test to gauge potential customer interest in Healthy Treats, as the budget does not

allow for research on both products. This test will cost $$2000.$ However, it cannot predict

market demand with absolute certainty. Past results indicate a $15\%$ chance of receiving a falsely

positive signal in a weak market and a $20\%$ chance of a falsely negative signal in a strong

market.

Despite the budget constraints limiting market tests to one product, there exists a notable

correlation in demand between Healthy Treats and Forever Youth. A high demand for Healthy

Treats corresponds to a $70\%$ likelihood of strong demand for Forever Youth, regardless of the

market test results. Similarly, if demand for Healthy Treats is low, there's a $60\%$ chance that

Forever Youth will also experience weak demand, independent of the market research

outcomes.

$($b$)$ PLEASE HELP TO Formulate the problem using a decision tree. Additionally, specify the probabilities required to

effectively solve and analyze the decision tree.

I have tried to create the decision tree but am unsure of my output. i have attached a screenshot of my decision tree please help to point out my mistake please. YOU CAN JUST DRAW A DECISION TREE SO THAT I CAN VERIFY MY MISTAKE $.$ PLEASE $...$