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# Quantitative Methods For Business Essay

1023 words - 5 pages

Question 1 (a)

Question 1 (b)
Revised probabilities for Survey study:
| Conditional Probability | | Posterior Probability |
State of Nature | P(Favourable result|State of Nature) | Prior Probability | Joint Probability | P(State of Nature|Favourable result) |
Successful Market | 0.70 | × 0.50 | = 0.35 | 0.350.45=0.78 |
Unsuccessful Market | 0.20 | × 0.50 | = 0.10 | 0.100.45=0.22 |
P(Favourable result) = | 0.45 | 1.00 |

| Conditional Probability | | Posterior Probability |
State of Nature | P(Unfavourable result |State of Nature) | Prior Probability | Joint Probability | P(State of Nature|Unfavourable result) |
...view middle of the document...

If the survey results are favourable, then Jim should produce the new razor or vice versa.

Utility Test

By using utility theory, the best decision is also “Conduct Survey” with a utility value of 0.82.

According to the utility test, it is found that Jim is a risk avoider as the utility curve above shows his preference of risk and his decision is on the highest EMV.
Question 2

To: CEO of Mt. Sinai Hospital
From: Tan Min Yee
Date: 8 November 2013
Subject: Presentation of optimal solution of 90-bed addition in the hospital

As a business analyst, I had observed and evaluated your structure of company. As instructed by you, I hereby present my report explaining the best option of proportioning the 90-beds addition for medical and surgical patients as well as other possibilities and cost factors.
Let abbreviation ‘m’= medical patients; ‘s’= surgical patients
(a) Profit maximisation = 2280m + 1515s
Optimal solution:
m= 2790.909, s= 2104.545
Profit maximisation = 2280(2790.909) + 1515(2104.545)
= \$ 9,551,659

The maximum revenue per year is \$ 9,551,659 with 2790.909 medical patients/year and 2104.545 surgical patients/year.
Medical patients = 2790.909
≈ 2791 people
Total number of hospital stay = 2791 × 8 days
= 22320 days
Number of beds required per year = 22320 days ÷ 365 days
= 61.15
≈ 61 beds

Surgical patients = 2104.545
≈ 2104 people
Total number of hospital stay = 2104 × 5 days
= 10520 days
Number of beds required per year = 10520 days ÷ 365 days
= 28.82
≈ 29 beds
Hospital stay: 8m + 5s ≤ 32850
Optimal solution:
m= 2790.909, s= 2104.545
Hospital stay: 8(2790.909) + 5(2104.545)
= 32,850

(b) Total beds required per year = 61 medical beds + 29 surgical beds
= 90 beds
Hence, there will be no empty beds available with this optimal solution. All 90 beds addition will be used up by both medical and surgical patients. There will not be a need of acquiring more beds. If more beds are acquired, Mt. Sinai Hospital will have immediate additional cost of purchasing more beds as well as additional cost in the x-ray department as serving more patients will...

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