Please give me a FULL explanation of why the correct answer

Please give me a FULL explanation of why the correct answer is point D and not point A. With examples if possible. Thanks!!

Butter Guns Figure 1: Production Possibilities Frontier for the U.S 3. For this question, refer to figure 1. At which point is the opportunity cost of Butter highest? Explain why. 5 points

Solution

If we look at the slope of the production possibility frontier in the figure, we can see that it is not constant and the opportunity cost keeps increasing for producing more guns while the opportunity cost keeps decreasing for producing more butter. This can be understood by observing the distance of the two ends of the curve from the origin of the graph (the vertex). We sacrifice guns for producing butter but the as we continue to produce more butter, the number of guns sacrificed keeps decreasing. Hence, the opportunity cost for producing butter is highest when we are producing the least quantity of butter. In this figure, the least quantity of butter is produced at point D. Hence, the opportunity cost of butter is highest at point D.