Answer :
In this case, with 3 scoops of ice cream, you would require a total of 6 cherries and 30 scoops of fudge.
To create a utility function for calculating the number of cherries and scoops of fudge based on the number of ice cream scoops, we'll use algebra to determine the relationship between the quantities of these items. We are given that for each scoop of ice cream (I), we require 2 cherries (C) and 10 scoops of fudge (F).
Now, let's express these requirements mathematically:
-[tex]\(C = 2 \times I\)[/tex] (since 2 cherries are needed for 1 scoop of ice cream)
-[tex]\(F = 10 \times I\)[/tex] (since 10 scoops of fudge are needed for 1 scoop of ice cream)
With these relationships, we can write the utility function \(U(I)\) that takes the number of ice cream scoops I as an input and returns the number of cherries C and scoops of fudge F needed. Thus, for a given quantity of ice cream scoops I, the function would be:
[tex]\[ U(I) = (C, F) \][/tex]
[tex]\[ U(I) = (2I, 10I) \][/tex]
Where:
-[tex]\(U(I)\)[/tex] is the utility function.
-I is the number of ice cream scoops.
-C is the number of cherries needed.
-F is the number of scoops of fudge needed.
For a practical example, if you have 3 scoops of ice cream I = 3 then according to the utility function [tex]\(U(I)\)[/tex]:
-[tex]\(C = 2 \times 3 = 6\)[/tex] cherries
-[tex]\(F = 10 \times 3 = 30\)[/tex] scoops of fudge
So with 3 scoops of ice cream, you would require a total of 6 cherries and 30 scoops of fudge.
