Multiply the production coefficient for Good X by the total labor force. For example, if you assume the production coefficient for Good X to be 4, and if you assume the total labor force to be 30, you would multiply 4 by 30, which gives 120. Thus, the maximum number of Good X your economy can produce is 120.
Draw a mark on the graphing paper at (120, 0). The x-axis represents the number of units produced of Good X, and the y-axis represents the number of units produced of Good Y. Notice that when your economy is producing 120 units of Good X, it is producing 0 units of Good Y.
Calculate the maximum number of Good Y your economy can produce, using the same method that was used for calculating Good X. For example, if the production coefficient for Good Y is 8, then you would multiply 8 by 30, which gives 240.
Draw a mark on the graphing paper at (0, 240). Again, notice how applying your whole labor force to Good Y production means that no one is working on Good X production.
Calculate the number of units produced if you allocate your labor force differently. For example, if you allocate 10 workers to produce Good X, and allocate the remaining 20 workers to produce Good Y, you would wind up with 40 units of Good X and 80 units of Good Y.
Plot the point (40, 80) on the graphing paper.
Repeat the previous two steps several times for different allocations of labor, until you get a satisfactory idea of what the curve will look like. Some production possibility curves are straight, some are concave and some are convex.
Draw a line from the y-axis to the x-axis that connects all the points you have plotted to see the production possibility curve.