Continuing on with my East Mercy Hospital Equation: I need to know how many beds
ID: 3178546 • Letter: C
Question
Continuing on with my East Mercy Hospital Equation: I need to know how many beds are required based on the State's guidelines. My instructor stated that the answers of 5, 1 and 3 were wrong for that portion. They were correct for the should add.
If you read this part: there are two answers required. How many to add and how many are required.
He stated to use invNorm.
When I calculated, the first one, I received an answer of 18 based on invNorm(.1627,24,6.1=18. Not sure if I used the correct data.
However, if I add the 5 to the 30 then calculate 5% of 35, I calculate 37 beds.
So I need assistance on how to solve this portion.
Original data:
East Mercy Medical Center is located in a rapidly growing area and is feeling capacity limitations. In particular, according to staff personnel, the obstetrics, adult medical surgical, and pediatric wards are “bursting at the seams.” East Mercy is considering an extensive expansion program, including expansion of the obstetric, adult medical surgical, and pediatric wards. The Board of Trustees has allocated $400,000 for new beds in these three wards. Megan Jacobs is recently hired as assistant administrator and is charged with determining how many beds current demand levels justify for each ward and how many beds to actually add, given the $400,000 cost constraint. Her staff computed statistics based on the current year’s patient census data in each of the three wards.
$15,500
East Mercy Medical Center is located in a rapidly growing area and is feeling capacity limitations. In particular, according to staff personnel, the obstetrics, adult medical surgical, and pediatric wards are “bursting at the seams.” East Mercy is considering an extensive expansion program, including expansion of the obstetric, adult medical surgical, and pediatric wards. The Board of Trustees has allocated $400,000 for new beds in these three wards. Megan Jacobs is recently hired as assistant administrator and is charged with determining how many beds current demand levels justify for each ward and how many beds to actually add, given the $400,000 cost constraint. Her staff computed statistics based on the current year’s patient census data in each of the three wards.
Ward Mean No. Beds Used Per Day Standard Deviation Present Capacity Cost of Adding 1 Bed + Supplies Obstetrics 24 6.1 30 $20,000 Surgery 13 4.3 20 $26,000 Pediatrics 19 4.7 24$15,500
Explanation / Answer
Let K1, K2, K3 be the number of beds added.
Let X1,X2,X3 be the demand for beds.
The cost constraint is
20,000 K1 + 26,000 K2 + 15,500 K3 <= 400,000
The other constraints are
P(X1 <= 30+K1) >= 0.95
24 + 1.65*6.1 <= 30+K1
K1 >= 4.03
P(X2 <= 20+K2) >= 0.95
13 + 1.65 * 4.3 <= 20 + K2
K2 >= 0.07
P(X3 <= 24+K3) >= 0.95
19 + 1.65 * 4.7 <= 24 + K3
K3 >= 2.73
The minimum number of beds to be added to the three departments are 5, 1 and 3 respectively.
The cost for this expansion is $22,000 * 5 + $26,000 * 1 + 15,500 * 3 = $100,000 + $26,000 + $46,500 = $172,500
The remaining fund can be made use of for further expansion.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.