Alctrex Construction Company is bidding against Betatrex for a building project. Due to past performance of both companies, Alctrex knows that if the company bids a lower or an equal amount, it will win the bid. It will cost Alctrex \(\$ 9,500\) to complete the project. Betatrex's bid is a random variable \(B\) with the following probabilities:

\[ \begin{aligned} & P(B=\$ 9,500)=0.45 \\ & P(B=\$ 10,500)=0.35 \\ & P(B=\$ 12,000)=0.20 \end{aligned} \]

Suppose that Alctrex is thinking of bidding between \(\$ 9,500\) and \(\$ 12,000\) in increments of \(\$ 500\). Determine the profit matrix for Alctrex. What is the best decision for the company? What is the value of perfect information?