Question

Six months before its annual convention, the American Medical Association (AMA) must determine how many rooms to reserve. At this time, the AMA can reserve rooms at a cost of $100 per room. The AMA believes the number of doctors attending the convention will be has a triangular distribution with minimum value 2000, maximum value 7000, and most likely value 5000. If the number of people attending the convention exceeds the number of rooms reserved, extra rooms must be reserved at a cost of $ 160 per room. Assume that there are 8000 rooms available.

[Round your answers to the nearest integer. Also just enter the number. For example, if your answer is $123,456, then enter 123456 without $ and comma.]

Q1) If they reserve 2,500 rooms now and the number of doctors attending the convention turns out to be 6,000, the number of extra rooms needed is?

Q2) If they reserve 6,000 rooms now and the number of doctors attending the convention turns out to be 2,000, the number of extra rooms needed is?

Q3)If they reserve 3,000 rooms now and the number of doctors attending the convention turns out to be 4,500, the total cost is?

Answer 1

Q1

Number of doctors who attended the convention = 6000

Number of reserved rooms = 2500

So, number of extra rooms needed is = 6000 - 2500 = 3500

Q2

Number of doctors who attended the convention = 2000

Number of reserved rooms = 6000

Since AMA have already reserved more rooms than the number of doctors who attended the convention, no extra room is needed.

Q3

Number of doctors who attended the convention = 4500

Number of reserved rooms = 3000

So, number of extra rooms needed is = 4500 - 3000 = 1500

Cost for the 3000 reserved rooms at the rate of $100 per room is = 3000 * $100 = $300000

Cost for the extra 1500 rooms at the rate of $160 per room is = 1500 * $160 = $240000

Hence, total cost is = $300000 + $240000 = $540000