The Local Mall Has a Make-Your-Own Sundae Shop

The local mall has a make-your-own sundae shop. They charge customers 35 cents for each fresh fruit topping and 25 cents for each processed topping. Barbara is going to make herself a sundae. The total utility that she receives from each quantity of topping is given by the following table:
Fresh Fruit Topping Processed Topping
# of Units Total Utility # of Units Total Utility
1 10 1 10
2 18 2 20
3 24 3 10
4 28 4 0
5 30 5 -10
6 28 6 -20
7 24 7 -30
8 18 8 -40
9 10 9 -50
10 -6 10 -60
a. What is the marginal utility of the 6th fresh fruit topping?
b. Of the two toppings, which would Barbara purchase first? Explain.
c. If Barbara has $1.55 to spend on her sundae, how many fresh fruit toppings and processed toppings will she purchase to maximize utility?
d. If money is no object, how many fresh fruit toppings and processed toppings will Barbara purchase to maximize utility?
e. Which of the basic assumptions of preferences are violated by preferences shown in the table above?