Note that the columns in this table all add up to 1. Explain why this happens.

Now, let pF, pT, pC, pCM, pSB denote the incomes of the Farmer, Tailor, Carpenter, Coal Miner and Slacker Bob, respectively. Note that each of these quantities not only denotes the incomes of each of our esteemed citizens, but also the cost of the corresponding goods. So for example, pF is the Farmer's income as well as the cost of all the food. So if the Farmer produces $100 worth of food, then his income will also be $100 since all of this food is bought out and the profits go to the Farmer.

The idea is, of course, to be able to figure out how should we price the goods in order for the citizens of Matrixville to survive; i. e. we must find pF, pT, pC, pCM, andpSB subject to the following conditions:

0.25pF + 0.15pT + 0.25pC + 0.18pCM + 0.20pSB = pF
0.15pF + 0.28pT + 0.18pC + 0.17pCM + 0.05pSB = pT
0.22pF + 0.19pT + 0.22pC + 0.22pCM + 0.10pSB = pC
0.20pF + 0.15pT + 0.20pC + 0.28pCM + 0.15pSB = pCM
0.18pF + 0.23pT + 0.15pC + 0.15pCM + 0.50pSB = pSB