A car resale company in Singapore is going to sell Tesla Model 3 in Singapore and Malaysia.
Question:
A car resale company in Singapore is going to sell Tesla Model 3 in Singapore and Malaysia. The company wants to reserve a number of vehicles six months ahead of the delivery. Based on a preliminary market survey, the company believes that the number of Tesla Model 3 sold per quarter in the two countries is normally distributed with a mean of 600 and a standard deviation of 80. The company can reserve the vehicles now (six months prior to the delivery date) for $50,000 each; however, three months later, for any vehicles ordered beyond the reserved now, the company will pay at the regular price of $59,000 each. The company will start to receive the customer orders three months later after a sales campaign. On the other hand, if some reserved vehicles cannot be sold in six months (i.e. nine months from now), the vehicles will be returned back to Tesla Asia Pacific distribution centre at Kuala Lumpur with a discounted refund of 80% of the reserved price each. The charge of 20% of the reserved price is used to pay the delivery fee, security and other business loss of the distribution centre.
Tasks:
1) Determine whether the car resale company should reserve 800, 900, 1000, 1100, 1200, 1300, 1400 or 1500 vehicles in advance to realize the lowest total cost using Crystal Ball.
2) Can you determine a more exact number or a small range of the number of vehicles to reserve to minimize the cost? Show your solution and evidence.