Each row of the table refers to one point on the production possibilities frontier. For example, if Alex chooses to spend all of his time producing picture frames, then he can produce four picture frames and zero cutting boards; so (4, 0) is one of the points on his initial PPF. Similarly, if he splits his time evenly between producing picture frames and cutting boards, he will produce two picture frames and 16 cutting boards; therefore, (2, 16) is another point on his initial PPF.

When using combination D, Alex is producing one picture frame and 19 cutting boards per day. Producing a second picture frame per day would require him to move to combination C, reducing his production of cutting boards to 16 per day. Since this change involves producing 3 fewer cutting boards per day (19−16=3$19-16=3$), the opportunity cost of producing the second picture frame per day is 3 cutting boards per day.

Similarly, using combination C, Alex is producing two picture frames and 16 cutting boards per day. Producing a third picture frame per day would require him to move to combination B, reducing his production of cutting boards to 11 per day. Since this change involves producing 5 fewer cutting boards per day (16−11=5$16-11=5$), the opportunity cost of producing the third picture frame per day is 5 cutting boards per day.

Alex's opportunity cost of producing the second picture frame per day is 3 cutting boards per day while the opportunity cost of producing the third picture frame per day is 5 cutting boards per day. Hence, as Alex increases his production of picture frames, his opportunity cost of producing more picture frames increases. This change is an example of the law of increasing opportunity costs.

The new tool causes Alex's PPF to pivot to the right. In other words, for each point on his PPF, the vertical coordinate is the same as before, but the horizontal coordinate is twice its initial value.

For example, under combination D, Alex spends 2 hours producing picture frames and 6 hours producing cutting boards. Before he bought the new tool, he could have produced one picture frame and 19 cutting boards, so (1, 19) was a point on his initial PPF. With the new tool, the same allocation of time results in two picture frames and 19 cutting boards, so (2, 19) is a point on his new PPF. Notice that one point is the same on the initial PPF and the new PPF. Because the new tool helps Alex make only picture frames, the tool does not change his output when he spends all of his time making cutting boards. This occurs at output combination E.

The shift in Alex's PPF is reflected in a corresponding change in his opportunity costs. Again, consider combination D, and consider the effects of moving from there to combination E. Both before and after Alex buys the tool, he can produce 19 cutting boards if he devotes 6 hours to producing them and 20 cutting boards if he devotes 8 hours to producing them. Therefore, spending his last 2 hours producing cutting boards results in one additional cutting board. Before he bought the tool, he would have to give up one picture frame. However, now that he has the tool, it means giving up two picture frames. Therefore, Alex's increased ability to produce picture frames increases his opportunity cost of producing cutting boards.