Q$-1)(50$ points$)$

Reconsider the California Manuf. Comp. example $($see the Week $11$ material on Teams$).$ In addition to LA and SF$,$ Irvine is also considered for building factory and perhaps a warehouse in that city. According to staff estimations, the profit of building a factory in Irvine is $\backslash (\backslash$$ $8\backslash )$ million and the amount of capital required to do this is $\backslash (\backslash$$ $4\backslash )$ million. The profit of building a warehouse there would be $\backslash (\backslash$$ $6\backslash )$ million and the capital required would be $\backslash (\backslash$$ $3\backslash )$ million. $($This option would be considered only if a factory also is being built there.$)$ The goal is to find the feasible combination of investments that maximizes the total profit, given that the amount of capital available for these investments is $\backslash (\backslash$$ $10\backslash )$ million.

Formulate a binary integer programming model for this problem.

Q$-2)(50$ points$)$

Solve the binary integer programming model you developed in Q$1$ using AMPL. Provide the optimal solution, the optimal value, the content of AMPL model file as well as the AMPL output.

Note: To define a binary variable in AMPL, use the command "binary". E$.$g$.$:

var x binary;