The Westfall Company has a contract to produce $10,000$ garden hoses for a large discount chain. Westfall has four different machines that can produce this kind of hose. Because these machines are from different manufacturers and use different technologies, their specifications are not the same.

$\backslash$table$[[$Machine$,\backslash$table$[[$Fixed Cost to$],[$Set Up$]],\backslash$table$[[$Variable Cost$],[$Per Hose$]],\backslash$table$[[$Capacity$],[($units$)]]],[1,$$$750,$$$1\mathrm{.}25,6000],[2,$$$500,$$$1\mathrm{.}50,7500],[3,$$$1000,$$$1\mathrm{.}00,4000],[4,$$$300,$$$2\mathrm{.}00,5000]]$

If machine $2$ is used, machine $3$ must be used also. However, if machine $3$ is used, machine $2$ need NOT be used.

The company wants to minimize the total cost of fulfill the contract. Please formulate a mixed integer linear programming problem to decide which machine$($s$)$ to use and how many garden hoses to produce on each machine if the machine is used.

The correct set of decision variables is: