Q$4)(6$ points$)$

The AD Company has a contract to produce $12,000$ Bikes for a customer. AD has four different processes that can assemble the Bike. The company would like to decide which processes to use for the assembly and how many bikes to assemble at each selected process. Processes specifications are as follows:

$\backslash$table$[[$Process$,$Fixed cost to setup the process,Variable cost per Bike,Process Capacity$],[1,$$$750,$$$1\mathrm{.}25,6000],[2,$$$500,$$$1\mathrm{.}50,7500],[3,$$$1000,$$$1\mathrm{.}00,4000],[4,$$$300,$$$2\mathrm{.}00,5000]]$

a$-$ Formulate the integer programming problem $($show full details$).$

b$-$ Write a constraint to ensure that if machine $2$ is used, then machine $3$ will not be used.

c$-$ Write a constraint to ensure that if machine $1$ is used, then machine $4$ must be used.