Based on the information given below, respond to questions $11$ and $14$

Alices an aspiring author, is considering pitching her book to a publishing house. The publishing house may decide to reject the book, but they may also choose to offer a publishing deal with either a one$-$year or two$-$year contract. Alice has two options: pitch her book and wait for the publishing house's decision or self$-$publish the book. The potential outcomes and corresponding proflts $($in thousands of dollars$)$ for different scenarios are as follows:

$\backslash$table$[[$State of Nature$],[$Decision Alternative,Reject, s$1,1$ Year, s$2,2$ Years, ss$,],[$Pitch Book, $d_1,-80,40,150,],[$Self$-$Publish, $d_2,,00,110,]]$

The probabilities for the states of nature are $P(s1)=0\mathrm{.}30,P(s2)=0\mathrm{.}30,$ and $P(s3)=0\mathrm{.}40.$ Alice also has the option to hire a literary agent who can evaluate the book's market potential for a fee of $$5000.$ Assume that the agency review will result in a favorable $(F)$ or an unfavorable $($U$)$ neview and that the following probabilities are relevant:

$P(F)=0\mathrm{.}69,P(s_1|F)=0\mathrm{.}11,P(s_1|U)=0\mathrm{.}41$

$P(U)=0\mathrm{.}31,P(s_2|F)=0\mathrm{.}33,P(s_2|U)=0\mathrm{.}24$

$,P(s_3|F)=0\mathrm{.}56,P(s_3|U)=0\mathrm{.}35$

$P(s_1|U)=0\mathrm{.}41$

$P(s_2|U)=0\mathrm{.}24$

$11.$ How much is EVPI in this decision$-$making problem? $(6$ points$)$

a$.16$

b$.29$

c$.24$

$($d$.)28$

$12.$ What is the recommended decision? $(8$ Points$)$

a$.$ No Agency, self$-$publish.

b$.$ No Agency, pitch book.

c$.$ hire a literary agent, if favorable self$-$publish, if unfavorable pitch book.

$($d$.$ hire a literary agent, if favorable pitch book, if unfavorable self$-$publish.

$13.$ How much is EVSI in this decision$-$making problem? $(6$ points$)$

a$.6\mathrm{.}1$

$($b$.)5\mathrm{.}8$

c$.7\mathrm{.}4$

d$.8\mathrm{.}4$

$14.$ What is the efficiency of the sample information survey $($agent evaluation$)?(5$ points$)$

a$.35\mathrm{.}2\%$

$($b$.)20\mathrm{.}7\%$

c$.34\mathrm{.}6\%$

d$.51\mathrm{.}9\%$