Instructions: Enter your answer as a whole number. If you are entering a negative number include a minus sign. Suppose that Biff enters a hot dog eating contest. He enjoys hot dogs, so he gladly pays the $$20$ entry fee. Biff realizes there is very little chance that he will actually win the contest. He just likes the idea of being able to eat all the hot dogs he wants. The table below shows Biff's utility from eating hot dogs.

Instructions: Enter your answers as a whole number. If you are entering a negative number include a minus sign.

a$.$ Use the table below and fill in the values for marginal utility.

Hot Dogs and Biff's Utility

$\backslash$table$[[\backslash$table$[[$Hot$],[$Dogs$]],\backslash$table$[[$Total Utility$],[($utils$)]],\backslash$table$[[$Marginal Utility$],[($utils$)]]],[5,48,-],[6,52,4],[7,54,2],[8,55,1],[9,54,-1],[10,51,-3]]$

b$.$ Use the table to graph Biff's total utility and marginal utility for hot dogs.

Instructions: Use the tool provided "Total Utility" to plot Biff" $s$ total utility point by point $(6$ points total$).$

Tools

Biff's Total Utility from Hot Dogs

Total UtilityInstructions: Use the tool provided "Marginal Utility" to plot Biff"s marginal utility point by point $(5$ points total$).$

Tools

Biff's Marginal Utility from Hot

Marginal Utility

Dogs

c$.$ If Biff is rational, and has no intention of winning the hot dog eating contest, what is the optimal number of hot dogs he will eat? What is the maximum level of utility Biff can reach from eating that number of hot dogs?

Optimal number of hot dogs:

Maximum utility