It is the night before your trip to Spain and you must decide how many hours to spend on expanding your vocabulary.

The total benefits column shows how many more Spanish words you expect to learn. The cost column shows how many Spanish words you will mispronounce because of the increased fast learning. (The “marginal” columns show the effect of each additional hour spent studying. These marginal numbers are calculated by taking the difference within a column from one row to the next row.)

Hours Spent Learning Total Benefit Marginal Benefit Total Cost Marginal Cost 0 0 – 0 –
1 8 8 0 0 2 13 5 2 2 3 16 3 6 4 4 16 0 12 6

a. If you study in an optimal way, how many more Spanish words will you learn?

b. Explain how you can find the optimal number of hours by using the marginal benefits and marginal costs columns.