Answer:
16
Explanation:
In economics, total utility (U) is the total satisfaction a consumer derived from consuming a commodity.
Under utility, there is what is called marginal utility (MU). Marginal utility is an extra utility a consumer derives from consuming an extra unit of a good.
Conditions under which consumer optimizes or maximizes his utility for a single good is different for two or more goods.
For one good, a consumer optimizes his utility when the MU of the good is equal price of the good. This can be expressed as follows:
MU(X) = P(X) ..................................... (1)
Equation (1) implies that MU of good X is equal to the price of good X, and the consumer optimizes his utility of good X at that point.
For two or more goods, a consumer optimizes his utility when the MU of all the goods are equal. Given two goods X and Y, for example, utility optimization of a consumer can be expressed as follows:
NU(X) = MU(Y) = ................................ (2)
Equation (2) implies that MU of good X is equal to the MU of good Y, and the consumer optimizes his utility at that point.
From the question, only one good which is hot dog-lemonade combo, C, is being considered. Therefore, the relevant equation to apply is equation (1).
Since total utility from C is given as follows:
................................ (3)
MU can be derived by differentiating equation (3) with respect C as follows:
....................... (4)
Recall that in equation (1), MU(X) = P(X), we follow the same thing and equate MU(C) in equation (4)to the price of C, P(C) as follows:
....... (5)
Since P(C) is equal to $5 from the question, we can substitute for it in equation (5) and solve for C as follows:
............................................. (6)
Squaring both sides of equation (6), we have:
C = 16
Therefore, Steve optimizes by consuming 16 meals
I wish you the best.