East Mercy Medical Center is located in a rapidly growing area and is feeling ca

Question

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     STANDARD     PRESENT    COST OF ADDING

                   USED PER DAY        DEVIATION    CAPACITY    1 BED + SUPPLIES

Obstetrics             24                          6.1                        30                      $20,000

Surgery               13                           4.3                        20                      $26,000

Pediatrics            19                           4.7                        24                      $15,500   

Histogram plots of bed usage show a remarkably close approximation to a normal distribution for each ward. Note that it is possible for a ward to exceed its capacity, but according to state guidelines, this should not occur more than 5% of the time.

Megan is in the process of preparing a report to the administrator showing how many beds are to be added to each of the three wards.

1. Has the EMMC Board set aside enough money to achieve this guideline?   Answer in a sentence.   

Explanation / Answer

Answer: The EMMC Board has set aside enough money to achieve the guideline.

Explanation:

The bed usage follows a normal distribution. Hence to allow the wards to exceed its capacity not more than 5%.

The capacity of each ward in the hospital should be able to satisy the bed usage 95 % of the times.

From normal distribution table, the no of beds should be at least mean usage + 1.644(q value at 95% probability) times the standard deviation.

Hence no of beds needed in each ward:

Obstetrics = 24 + 1.644*SD = 24 + 1.644*6.1 = 34.03~ 34 beds

Present capacity = 30 beds.

Hence extra beds needed = 34 - 30 = 4 beds

Cost = $20,000 * 4 = $80,000

Working out similarily:

Surgery: 13 + 1.644*4.3 = 20.069 ~ 20 beds

Present capacity is also 20 beds . Hence no extra beds required

Pediatrics: 19 + 1.644*4.7 = 26.73 ~ 27 beds

Hence extra beds required : 27 - 24 = 3 beds

Cost : $15,500 * 3 = $46,500

Hence total costs of adding required beds in all wards: $80,000 + $46500 = $126,500

This is much less than the cost constraint. Hence it is safe to say that the EMMC Board has set aside enough money to achieve the guideline

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