A large steel manufacturing company has three options with regard to production: (1) produce commercially (ii) build pilot plant (iii) stop producing steel. The management has estimated that their pilot plant, if built, has 0.8 chance of high yield and 0.2 chance of low yield. If the pilot plant does show a high yield, management assigns a probability of 0.75 that the commercial plant will also have a high yield. If the pilot plant shows a low yield, there is only a 0.1 chance that the commercial plant will show a high yield. Finally, management's best assessment of the yield on a commercial - size plant without building a pilot plant first has a 0.6 chance of high yield. A pilot plant will cost LKR 0.3 Million. The
profits earned under high and low yield conditions are LKR 12 Million and LKR 1.2 Million respectively. Find the optimum decision for the company
Answers
Answer:
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Answer:
The optimum decision for the company will be that the company should not build the pilot plant but should produce commercially.
Step-by-step explanation:
The decision tree diagram has been represented in the figure.
EMV of chance node C will be = Rs. [0.75(1,20,00,000)-0.25(12,00,000)]
= Rs. 87,00,000
EMV of chance node D will be = Rs. [0.1(1,20,00,000)-0.9(12,00,000)]
= Rs. 1,20,000
EMV of decision node 2 is = Rs. 87,00,000
EMV of decision node 3 is = Rs. 1,20,000
EMV of chance node A will be = Rs. [0.8(87,00,000)-0.2(1,20,000)]
= Rs. 69,36,000
The EMV of decision node 1 if pilot plant is built:
= Rs. [69,36,000-3,00,000]
= Rs. 66,36,000
EMV of chance node B will be:
= Rs. [0.6(1,20,00,000)-0.4(12,00,000)]
= Rs. 67,20,000
So, EMV of decision node 1 for alternative 'produce commercially' will be:
= Rs. 67,20,000
Therefore, the optimum decision for the company will be that the company should not build the pilot plant but should produce commercially.
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