A boutique chocolate manufacturer produces 2 types of chocolate, Dark chocolate, and Milk chocolate daily with a total cost function: TC = 7D+Dx M + 3M where: D is the quantity of the Dark chocolate (in kgs) and M is the quantity of the Milk chocolate (in kgs). The prices that can be charged are determined by supply and demand forces and are influenced by the quantities of each type of chocolate according to the following equations: PD = 20-D + 5M for the price (in dollars per kg) of the Dark chocolate and PM 23 + 3D - M for the price (in dollars per kg) of the Milk chocolate. The total revenue is given by the equation: TR= PD XD + PM X M 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 D and M only. Using the method of Lagrange Multipliers find the maximum profit when total production (quantity) is restricted to 2023 kgs. Note D or M need not be whole numbers. Be sure to show that your solution is a maximum point.

A boutique chocolate manufacturer produces 2 types of chocolate, Dark chocolate, and Milk chocolate daily with a total cost function: TC = 7D+Dx M + 3M where: D is the quantity of the Dark chocolate (in kgs) and M is the quantity of the Milk chocolate (in kgs). The prices that can be charged are determined by supply and demand forces and are influenced by the quantities of each type of chocolate according to the following equations: PD = 20-D + 5M for the price (in dollars per kg) of the Dark chocolate and PM 23 + 3D - M for the price (in dollars per kg) of the Milk chocolate. The total revenue is given by the equation: TR= PD XD + PM X M 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 D and M only. Using the method of Lagrange Multipliers find the maximum profit when total production (quantity) is restricted to 2023 kgs. Note D or M need not be whole numbers. Be sure to show that your solution is a maximum point.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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