When there is only one factor of production the production possibility frontier of an economy is simply a straight line. We can derive this line as follows: if Q_W is the economy’s production of wine and Q_C its production of cheese, then the labor used in producing wine will be a1wQw the labor used in producing cheese a1cQc. The production possibility frontier is determined by the limits on the economy’s resources – in this case, labor. Because the economy’s total labor supply is L, the limits on production are defined by the inequality
a_LC Q_C+a_LW Q_W ≤L