Bottles of Soda Slices of Pizza

-The table above gives Ali's total utility from consuming bottles of soda and slices of pizza.The price of pizza is $2 per slice and the price of soda is $1 per bottle.Ali has $14 in his budget.When Ali maximizes his utility he buys ________ bottles of soda and ________ slices of pizza.
A) 4; 5
B) 6; 4
C) 2; 6
D) 6; 6
E) None of the above answers is correct.

Question

Bottles of Soda	Slices of Pizza
 
-The table above gives Ali's total utility from consuming bottles of soda and slices of pizza.The price of pizza is $2 per slice and the price of soda is $1 per bottle.Ali has $14 in his budget.When Ali maximizes his utility he buys ________ bottles of soda and ________ slices of pizza.
A) 4; 5 
B) 6; 4 
C) 2; 6 
D) 6; 6 
E) None of the above answers is correct.

Quizplus · Accepted Answer

Ali's budget constraint is 14 = 2P + S, where P is the number of slices of pizza and S is the number of bottles of soda. Substituting the prices, we get 14 = 2P + S. Solving for S, we get S = 14 - 2P.Ali's utility function is U(P, S) = P^0.5 * S^0.5. Substituting the budget constraint, we get U(P, S) = P^0.5 * (14 - 2P)^0.5. Taking the derivative of U with respect to P, we get dU/dP = 0.5P^-0.5 * (14 - 2P)^0.5 - P^0.5 * 0.5 * (14 - 2P)^-0.5 * (-2) = 0.5P^-0.5 * (14 - 2P)^0.5 + P^0.5 * (14 - 2P)^-0.5. Setting dU/dP = 0, we get 0.5P^-0.5 * (14 - 2P)^0.5 + P^0.5 * (14 - 2P)^-0.5 = 0. Solving for P, we get P = 4. Substituting P = 4 into the budget constraint, we get S = 14 - 2P = 14 - 2(4) = 6.Therefore, Ali maximizes his utility by buying 4 bottles of soda and 6 slices of pizza.