recall that Casper's utility function is 3x  y, where x is his consumption of cocoa and y is his consumption of cheese.If the total cost of x units of cocoa is x², the price of cheese is $2, and Casper's income is $39, how many units of cocoa will he consume?

A) 5
B) 0
C) 2
D) 3
E) 6

We need to maximize Casper's utility function subject to his budget constraint.
His budget constraint is: x² + 2y = 39
We can rearrange it as: y = (39 - x²)/2
Substituting y in the utility function, we get:
U(x) = 3x  (39 - x²)/2
To maximize U(x), we need to find the value of x that maximizes the above function.
Differentiating U(x) with respect to x and setting it equal to zero, we get:
3  (39 - 2x²)/2 = 0
Simplifying, we get:
39 - 2x² = 0
x² = 19.5
x = 3
Therefore, Casper will consume 3 units of cocoa.