$7.$ The Miramar Company in Problem $6$ is considering contracting with a market research firm to do a survey to determine future market conditions. The results of the survey will indicate either positive or negative market conditions. There is a $\mathrm{.}60$ probability of a positive report, given favorable conditions; a $\mathrm{.}30$ probability of a positive report, given stable conditions; and a $\mathrm{.}10$ probability of a positive report, given unfavorable conditions. There is a $\mathrm{.}90$ probability of a negative report, given unfavorable conditions; a $\mathrm{.}70$ probability, given stable conditions; and a $\mathrm{.}40$ probability, given favorable conditions.

$(1)$ Using decision tree analysis and posterior prob$-$ability tables, determine the decision strategy the company should follow, the expected value of the strategy, and the maximum amount the company should pay the market research firm for the survey results.

$(2)$ Compute the efficiency of the sample information.