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Mick Karra is the manager of MCZ Drilling Products, which produces a variety of specialty valves for oil field equipment. Recent activity in the oil fields has caused demand to increase drastically, and a decision has been made to open a new manufacturing facility. Three locations are being considered, and the size of the facility would not be the same in each location. Thus, overtime might be necessary at times. The following table gives the total monthly cost $($in $$1,000$ s$)$ for each possibie location under each demand possibility. The probabilities for the demand levels have been determined to be $20\%$ for low demand, $30\%$ for medium demand, and $50\%$ for high demand.

$\backslash$table$[[,$DEMAND IS LOWDEMAND IS MEDIUMDEMAND IS HIGH,,$],[$Ardmore$,$ OK$,85,110,150],[$Sweetwater$,$ TX$,90,100,140],[$Lake Charles, LA$110,120,130,]]$

What is the expected value of perfect information in this situation?

Select one:

a$.$ $$8$

b$.$ $$4$

c$.$ $$6$

d$.$ $$10$