How to decide an Objective Function?


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In the Njaba river basin, the available water was allocated for the purposes of consumption, irrigation, and electric power supply among three communities. The water allocated per annum per capita for all use in these communities are 10m3 , 10m3 and 30m3 . The allocations were made based on the critical factors of population, land area and the industrialization. The populations of the communities are 300, 200, and 100, power supply capacities are 20W, 10W and 20W while the land areas for irrigation are 50 hectares, 40 hectares, and 30 hectares respectively. Allowable allocations limits of more than 300, 100 and 80 were stipulated for the purposes. Using the above information, formulate, (a) Linear Programming Model for the basin. (b) Maximization the allocations made Assume non-negativity condition?

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I’m learning this course for the very first time so for understanding this subject and it’s problems, I’m trying to solve different problems. I’m recently solving this problem showing above. As it is a solved example I found on the internet, here’s the objective function and constraints.

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Let the three communities be denoted by the variables x, y, and z. The objective function should be based on the allocation per annum, per capita for the basin as stated;

Z = 10x + 10y + 30z

The constraints can be formulated thus;

300x + 200y + 100z > 300 20x + 10y + 20z > 100 50x + 40y + 30z > 80

Under the negativity conditions of

X, Y, Z > 0

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My confusion is writing an objecting function in this question. When different communities are supplied water for different use then it’s obvious that usage of water in every community for different use is different. Like annually, per person usage of water would be different. If a person is using water only for domestic need the whole year, they are nothing to do with the irrigation and electric power supply so how could this line be justifiable that

*The water allocated per annum per capita

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for all use

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in these communities are 10m3 , 10m3 and 30m3 *?

like every single person is allocated water for all uses like for basic consumption, irrigation, electric power supply means they’re providing extra water?

Hope so everyone is getting my question and will sort out my query so I better solve questions on my own.