Question 1 A boutique fruit juice manufacturer produces 2 types of juices, Apple and Fig daily with a total cost function: TC = 6A + A x F +9F where: A is the quantity of the Apple juice (in kegs) and F is the quantity of the Fig juice (in kegs). The prices that can be charged are determined by supply and demand forces and are influenced by the quantities of each type of juice according to the following equations: P₁ = 17-A + F for the price (in dollars per keg) of the Apple juice and PF = 23 + 2A-F for the price (in dollars per keg) of the Fig juice. The total revenue is given by the equation: TR = PAX A+ PF XF and the profit given by the equation Profit= TR-TC First, use a substitution of the price variables to express the profit in terms of A and F only. Using the method of Lagrange Multipliers find the maximum profit when total production (quantity) is restricted to 2023 kegs. Note A or F need not be whole numbers. Be sure to show that your solution is a maximum point.

Question 1 A boutique fruit juice manufacturer produces 2 types of juices, Apple and Fig daily with a total cost function: TC = 6A + A x F +9F where: A is the quantity of the Apple juice (in kegs) and F is the quantity of the Fig juice (in kegs). The prices that can be charged are determined by supply and demand forces and are influenced by the quantities of each type of juice according to the following equations: P₁ = 17-A + F for the price (in dollars per keg) of the Apple juice and PF = 23 + 2A-F for the price (in dollars per keg) of the Fig juice. The total revenue is given by the equation: TR = PAX A+ PF XF and the profit given by the equation Profit= TR-TC First, use a substitution of the price variables to express the profit in terms of A and F only. Using the method of Lagrange Multipliers find the maximum profit when total production (quantity) is restricted to 2023 kegs. Note A or F need not be whole numbers. Be sure to show that your solution is a maximum point.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter14: Monopoly

Section: Chapter Questions

Problem 14.13P

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