Venture Fair$)$ In order to participate at a venture fair, Team TerraZ is preparing a project plan for their new$-$product offering. The team plans to spend $3$ days on ideation. Once ideation is complete, the team aims to interview $20$ potential customers $(6$ days$)$ and to engage in a careful analysis of competing products $(12$ days$).$ Following the customer interviews, the team expects to spend $10$ days on careful user observation and $4$ days on sending out e$-$mail surveys. These two activities are independent from each other, but both require that the interviews be completed. With the input from the customer observation and the e$-$mail surveys, the team then plans to spend $5$ days on putting together the target specifications for the product. This activity also requires the analysis of competing products to be complete. After the target specifications, the team aims to create a product design, which will take $10$ days. With the product design complete, they plan to get price quotes $(6$ days$)$ and build a prototype $(4$ days$)$ that they then want to test out with some customers $(5$ days$).$ Once the prototype has been tested and the price quotes are in$,$ they can put together their information material for the venture fair $(3$ days$).$ a$.$ Create a dependency matrix for the activities described, and build a project graph. $[12,1]$ b$.$ Find the critical path. What is the latest time the team can start working, assuming the venture fair is scheduled for April $18?[12\mathrm{.}4]$