UK climate projections suggest a change in rainfall patterns.This will increase risk of flooding of cities from rivers. As amitigation, a local lead flood authority is considering replacingthe current temporary flood barriers with three different permanentgates to control the flood in different flood situations. The timerequired to complete each, and the number of workers required to beon the job at all times are shown in Table A below.
Table A. Specification ofthe flood barrier projects
Flood barrier gate - Duration of work [months] - Number ofworkers required
1 - 2 - 30
2 - 2 - 20
3 - 3 - 30
Once a flood gate is completed, it is estimated that it cancontrol the following amount of water measured in cubic metres permonth (cmm): gate I, 50cmm; gate 2, 30cmm; gate 3, 40cmm. Forbuilding these three gates, 60 workers are available during eachmonth.
(a) Formulate a mathematical model in order to maximise, in thecase of flood, the total water control capacity at the end of month4.
(b) Formulate the following additional constraints forced by thetlood management committee:
(i) At most, construction on only one gate can be started duringanyone month.
(ii) Gate 2 must be completed by the end of month 4.
