Mathematics desk
< November 13	<< Oct \| November \| Dec >>	November 15 >

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

November 14

Drought Relief

In South Africa currently there are droughts in the West and flooding in the East. Please would you assist with the following calculations. How much would it cost to alleviate the problem. Mt idea is to truck water from the flooded parts to the drought-stricken parts. I have gained the following statistics. An average farm needs 55 L of water per head of cattle per day (maximum, mother with calf). The cost of petrol in South Africa is currently R13.79 per L. The minimum wage to pay the drivers is R20.00 per hour. The drive could be up to 15 hours per truck. The distance would be up to 1,500 km. a water truck capacity is about 43,900 L. The water would not need to be sanitised as it will be watering crops, theoretically. So, we pay X number of people to pump water and fill the trucks. This takes Y amount of time. We then truck water from the far east to the far west. Please calculate cost. Thanks. Anton 81.131.40.58 (talk) 10:45, 14 November 2019 (UTC)[reply]

Some other factors to consider:

The cost of the return trips. If there was something else they could ship the other way, without having to clean out the tanks, that would defray this cost.
Acquisition of the trucks. If they are even available, you would need to buy them or rent them. Quite possibly you also would need to ship them to South Africa.
The wear and tear on the truck, in the form of maintenance, towing, etc., that will be required.
If the trucks last hauled something toxic, they will need to be washed out. This may require detergent, depending on the substance hauled.
The time delay. By the time you organize everything, the floods and/or drought could be over. SinisterLefty (talk) 10:56, 14 November 2019 (UTC)[reply]

The drought has been ongoing for 5 years now. Let us assume I can source a donation of trucks for the time required, so rent free. The trucks are already in South Africa, so no need to ship them there. Cleaning, I would expect 20% of the trucks to need deep cleaning with detergent. let us assume 1 day per truck plus to men at minimum wage plus detergent we will get donated free of cost. Wear and tear is also not a concern as I will source these from a donation or rent free use for the needed period of time. Time delay? I specialise in getting things done in a timely manner. I just want the rough calculation and formulae used so that as and when other factors need to be included I can add these in. Thanks for your help. Anton 81.131.40.58 (talk) 11:53, 14 November 2019 (UTC)[reply]

Pretty sure what you need is a spreadsheet, the calculations aren't difficult but a spreadsheet will help organize all the data being used. One variable you didn't specify was truck mileage, I'm going to assume 5km/L. Putting all this into a spreadsheet of my own I get:

Desc				Value		Units
Water needed			55		L/day/head
Distance			1500		km
Truck mileage			5		km/L
Fuel per round trip		600		L
Fuel cost			13.79		R/L
Fuel cost per round trip	8274		R
Driver Pay			20		R/H
Drive time			15		H
Driver cost per round trip	600		R
Total cost per round trip	8,874		R
Truck Capacity			43,900		L
Trips Needed			0.00125284738	/day/head
Total cost			11.11776765	R/day/head

I used Google Sheets in this case because it's free, doesn't require download, and does the job. --RDBury (talk) 13:50, 14 November 2019 (UTC)[reply]

Thank you so much for this. I have used your spreadsheet idea and have rounded off the figures to the highest round figure. Please would someone check my calculations, but I expect that with 150,000 km2 of farmland in the Northern Cape and 10 km2 watered per trip with 3,500 L needed per km2 of farmland, we would need 12,000 trips at a cost of R20,000.00 each resulting in a cost of £250,000,000.00 per week. So with an estimated 1bn per month we can resolve the drought issue. This being in South African Rands we can divide by 17 for a UK exchange rate and say that this could be resolved with £58,823,529.41 per month. Kindly clarify or confirm. Thank you Anton 81.131.40.58 (talk) 15:06, 14 November 2019 (UTC)[reply]

Was the cost of the return trips included ? Also, 3500 L per km² seems extremely low. That's only .0035 L per m². (A km² contains (1000 m)² = 1000² m², or one million m².) SinisterLefty (talk) 16:46, 14 November 2019 (UTC)[reply]

Truck maintenance and amortization is expensive, you'll probably have to double the fuel costs or more (and I think 20 L/100 km is fairly low for a tanker semi, especially as old as African trucks probably are). You also need to filter flood waters, as they're disgusting. Tho you could get rid of the 2nd problem by building some dams and carting off excess water from accumulation lakes. 93.136.94.213 (talk) 07:15, 17 November 2019 (UTC)[reply]

Clarification on https://en.wikipedia.org/wiki/Evolutionarily_stable_strategy

How does "Harm Thy Neighbor game" and "Harm Everyone game" work? On "Harm Thy Neighbor, how is it that (A,A) is considered to be a Nash Equilibrium? Both payoffs for Column player are the same, so the chance that the column player will choose either A or B when row player chooses A is 1/2. Analyzing it using IESDS ( Iterated Elimination of Strictly Dominated Strategies) will yield (B,B) as a Nash Equilibrium. Analyzing it using Maximin will still yield (B,B).120.29.85.245 (talk) 18:46, 14 November 2019 (UTC)[reply]

Neither player has an incentive to switch away from (A,A) in isolation. This is the definition of a Nash Equilibrium.--101.100.158.248 (talk) 08:38, 16 November 2019 (UTC)[reply]

Yes, Nash equilibrium is in essence an unimprovable strategy against another player playing this equilibrium strategy. It says nothing about being unimprovable against players who choose to play some other strategy, which is what I gather the point of ESS is. 93.136.94.213 (talk) 07:08, 17 November 2019 (UTC)[reply]

An ESS is a population-level concept: it shows what happens if a population of players using one strategy are (for example) invaded by players using another strategy. The strategies themselves may be Nash Equilibria, although this is not required. The idea is to capture whether a given strategy is stable to random "mutations" in the available/chosen strategies: for example, a society where every player is 100% altruistic to the player to his immediate right works great so long as everyone keeps playing it; however, if one player decides to be 100% selfish, he can wreak havoc on everyone else. OldTimeNESter (talk) 16:25, 18 November 2019 (UTC)[reply]