Please write clearly or use the computer to type the answer so that I can see it clearly, thank you!!!

Please show the step

There is a two-stage make-to-order (MTO) supply chain that has an alcohol-based hand sanitizing gel manufacturer in China and a distributor in the United States (US). The US distributor purchases the gel from the Chinese manufacturer at the cost of $20 per bottle and sells at the price of $30 per bottle in an online trade fair. The manufacturer has set the purchase lot size as 2,000 bottles. The distributor can sell all unsold products to a discount store at $5 per bottle. The distributor has forecasted the product demand in the upcoming online trade fair (see the table below).

For the Chinese manufacturer, the fixed production cost is $10,000 and variable production cost is $10 per box. The US distributor has determined that its expected profit equals to $80,000 if order quantity is 8,000 bottles and $87,500 if order quantity is 10,000 bottles. Show the units and steps of calculation when you answer the following questions.

(a1) Determine the expected profit for the US distributor if order quantity is 12,000 bottles, and the optimal order quantity that will maximize the distributors profit.

(a2) If the distributor adopts the optimal order quantity of (a1), determine the manufacturers profit.

Demand (bottles) 8,000 10,000 Probability (%) 252 30 12,000 452