Question 1A boutique fruit juice manufacturer produces 2 types of juices, Apple and Fig daily with a total costfunction: TC = 6A + A × F +9Fwhere:A is the quantity of the Apple juice (in kegs) andF 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 bythe 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 andPF = 23+2A-F for the price (in dollars per keg) of the Fig juice.The total revenue is given by the equation:TR = PAXA + PF XFand the profit given by the equationProfit = TR - TCFirst, 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.

Lagrangian optimization problem has a following setup : Objective function & Constraint…

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 P = 23+2A-F for the price (in dollars per keg) of the Fig juice. TR= P. The total revenue is given by the equation: P. X F

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 P = 23+2A-F for the price (in dollars per keg) of the Fig juice. TR= P. The total revenue is given by the equation: P. X F

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter18: Asymmetric Information

Section: Chapter Questions

Problem 18.3P

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