A primitive economy depends on two basic good yams and pork

A primitive economy depends on two basic good, yams and pork. Production of 1 bushel of yams requires 1/6 bushels of yams and 1/3 of a pig. To produce 1 pig requires 1/2 bushel of yams. Find the amount of each commodity that should be produced to get 100 bushels of yams and 70 pigs.

Solution

= represents requirement for production.

1 bushel of yams = 1/6 bushel of yams + 1/3 bushels of pig

100 bushels of yams = 100/6 bushels of yams + 100/3 bushels of pig

1 bushel of pig = 1/2 bushels of yams = 1/12 bushel of yams + 1/6 bushels of pig

70 bushels of pig = 70/12 bushels of yams and 70/6 bushels of pig.

Thus number of bushels of yams required = 100/6 + 70/12 = 135/6 = 23

Number of bushels of pigs required = 100/3 + 70/6 = 45