is responsible for evaluating and choosing which R$\backslash$&D projects to support. The company received $18$ R$\backslash$&D proposals from its scientists and engineers, and identified six $(6)$ projects as being consistent with the company's mission. However, the company does not have the funds available to undertake all six projects. Mark must determine which of the projects to select. The capital requirements for each project are summarized in the following table along with the expected profit the company expects each project to generate.

The company has total capital of $300($in thousands$)$ available to invest.

Due to synergies between various project and company's future direction, Mark must decide to invest in project $4$ if he decides to invest in project $6.$ Similarly, Mark should only invest in project $2,$ if he decides to invest in project $3.$

Finally, due to extreme differences in nature, Mark cannot simultaneously invest in project $1$ and project $2$ together.