Let f, t, c, m, and b denote the incomes of the farmer, tailor, carpenter, miner, and Bob, respectively. Note that each of these quantities represents not only the gross incomes of each of our citizens but also the total cost of the goods they sell. So for example, f is the farmer's income and also is the cost of all the food. If the farmer produces $100 worth of food, then his income will also be $100, since all of this food gets purchased and all the revenue goes 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, and pSB 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