Quantitative Methods for Business

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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) | Successful Market | 0.30 | × 0.50 | = 0.15 |…show more content…
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 results in handling more x-rays. This optimal solution will use up its maximum unutilized capacity of 7,000 more x-rays. (c) Laboratory tests: 3.1m + 2.6s ≤ 15000 Optimal solution: m= 2790.909, s= 2104.545 Laboratory tests: 3.1(2790.909) + 2.6(2104.545) = 14123.63 ≈ 14124 The laboratory is not utilized to its maximum capacity. The laboratory is capable of handling another 15,000 tests per year. In this optimal solution, there will be another 14,124 lab tests only. Hence, it is able to perform 876 more lab tests (15,000-14,124) per year. If Mt. Sinai Hospital acquires more lab space, there will be no additional cost until it reached its maximum capacity of 15,000 additional lab tests. However, there will be additional cost if it exceeds its maximum capacity. (d) X-ray: 1m + 2s ≤ 7000 Optimal solution: m= 2790.909, s= 2104.545 X-ray: 1(2790.909) + 2(2104.545) = 7000 The x-ray facility is being used to its maximum of 7,000 x-rays in this optimal solution. The x-ray department could not perform more than additional 7,000 x-rays per year without significant additional cost. If Mt. Sinai Hospital acquires more x-ray facilities, a significant additional cost would be incurred which is not favourable. (e) Operating room:
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