The Quality Control Manager for the NKA Inc Based on Historical Data,if the Lot Is of Poor Quality,40

The quality control manager for the NKA Inc.must decide whether to accept (alternative 1),further analyze (alternative 2),or reject (alternative 3)the shipment (lot)of incoming material.The historical data indicates that there is 30% chance that the lot is poor quality (S₁),50% chance that the lot is fair quality (S₂),and 20% chance that the lot is good quality (S₃).Assume the following payoff table is available.The values in the payoff table are in thousands of dollars. $$\begin{array} { l c c c } & { \text { States of Nature } } \\\text { Decision } & \mathrm { S } _ { 1 } & \mathrm {~S} _ { 2 } & \mathrm {~S} _ { 3 } \\\text { Accept } & 20 & 30 & 90 \\\text { Further analyze } & 60 & 70 & 15 \\\text { Reject } & 80 & 50 & 30\end{array}$$ Based on historical data,if the lot is of poor quality,40% of the items are defective.If the lot is fair quality,22% of the items are defective.If the lot is good quality,10 % of the items are defective.The quality control manager inspects one unit from a recent shipment.
-A company wants to add a new product to its existing line of products.There are two similar candidate products A and
B.The demand for the new product could be high,medium,or low with probabilities of .25,.5,and .25 respectively.The demand and the corresponding profit for each product is: $$\begin{array} { | l | l | l | l | } \hline & \text { High } & \text { Medium } & \text { Low } \\\hline \text { Product A } & 40,000 & 30,000 & 20,000 \\\hline \text { Product B } & 70,000 & 20,000 & 0 \\\hline\end{array}$$ Which product should the company select based on the expected monetary value criterion?
Product A has a higher expected monetary value
A Expected monetary value = .25(40000)+ .5(30000)+ .25(20000)= 30,000
B Expected monetary value = .25(70000)+ .5(20000)+ .25(0)= 27,500