Case study

A college student, SK$,$ recently took a course in management sciences. He now enjoys applying what he learned to optimize his personal decisions. He is currently analyzing one such decision: how much money $($if any$)$ to withdraw from his savings account to purchase $$100$ traveler's checks before leaving for a short vacation trip to Europe next summer.

SK has already used the funds he had in his checking account to purchase traveler's checks worth $$1,200,$ but he is uncertain if this amount will be sufficient. In fact, he has estimated the probability distribution of his potential expenses, as shown in the following table:

$\backslash$table$[[$Amount needed $($$$),1000,1100,1200,1300,1400,1500,1600,1700],[$Probability$,0\mathrm{.}05,0\mathrm{.}1,0\mathrm{.}15,0\mathrm{.}25,0\mathrm{.}2,0\mathrm{.}1,0\mathrm{.}1,0\mathrm{.}05]]$

If SK finds himself with a shortfall in funds, he will have to cut his trip short by one day for every $$100$ he is lacking. Since he values each day in Europe at $$150,$ each day lost would result in a net loss of $$50$ for him. However, purchasing an additional $$100$ traveler's check incurs an additional cost of $$1.$ In addition, any unused traveler's checks at the end of the trip would result in a loss of $$2$ in interest that could have been earned in his savings account during the trip. Therefore, SK does not want to purchase an excessive amount of traveler's checks.