Writing and Objective Function and Linear Constraints The owner of a chain of amusement parks has to make some decisions Suppose there is a start up cost of operatingan amusement parkfortheday Ifamusement park 1isoperated,thenthereisafixedstart upcostof A Similarly, for amusement parks 2 and 3 there are fixed start up costs A ,A , respectively To model this, weintroducebinaryvariables , , thatshouldrepresentwhetheramusement park1,2,and3respectively,arebeingoperated Writelinear constraintsthatenforcethatifthestart upcosts arenotpaid, then theamusement park cannotoperate Thatis,if is0,then isalso0 Otherwise,if is1,then can take any value Writeanewobjectivefunction thatincorporatesthestart upcosts To simplify the employee availability constraint, we want to enforce a constraint so that at most oneofthe amusement parks1and2 (both large amusement parks)canoperate duringtheentire day Writealinear constraintto enforce this Write a linear constraint using only variables , , enforcing that amusement park 1 cannotbetheonlyamusement park operated(inotherwords, ifamusement park1isused, thenatleastoneof amusement parks 2 and 3 must also be operated)

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Writing and Objective Function and Linear Constraints: The owner of a chain of amusement parks has to make some decisions. Suppose there is a start-up

Writing and Objective Function and Linear Constraints:

The owner of a chain of amusement parks has to make some decisions. Suppose there is a start-up cost of operatingan amusement parkfortheday.Ifamusement park 1isoperated,thenthereisafixedstart-upcostof A_!.Similarly, for amusement parks 2 and 3 there are fixed start-up costs A_",A_#, respectively. To model this, weintroducebinaryvariables_!,_",_#thatshouldrepresentwhetheramusement park1,2,and3respectively,arebeingoperated.

Writelinear-constraintsthatenforcethatifthestart-upcosts arenotpaid, then theamusement park cannotoperate.Thatis,if_!is0,then_!isalso0.Otherwise,if_!is1,then_!can take any value.
Writeanewobjectivefunction thatincorporatesthestart-upcosts.
To simplify the employee availability constraint, we want to enforce a constraint so that at most oneofthe amusement parks1and2 (both large amusement parks)canoperate duringtheentire day.Writealinear-constraintto enforce this.
Write a linear-constraint using only variables _!,_",_#enforcing that amusement park 1 cannotbetheonlyamusement park operated(inotherwords, ifamusement park1isused, thenatleastoneof amusement parks 2 and 3 must also be operated).