pes of beers, Dark-ale and Light-ale daily ith a to que beer Br very produces 2 function given by TC = 8D + DXL +3L where D is the quantity of Dark-ale beer (in kegs) (not kg), and L is the quantity of Light-ale beer (in kegs) The prices that can be charged are determined by supply and demand forces and are influenced by the quantities of each type according to the following equations: PD=53-D + L for the price $/keg for Dark-ale beer PL= = 42 + 2D - L for the price $/keg for Light-ale beer The total revenue is given by the equation: TR = PD X D + P₁ X L And the profit given by the equation: Profit = TR - TC (a) Write down the profit in terms of D and L only. (b) The total production (quantity) of both beers combined is restricted to 191 kegs. Formulate th
pes of beers, Dark-ale and Light-ale daily ith a to que beer Br very produces 2 function given by TC = 8D + DXL +3L where D is the quantity of Dark-ale beer (in kegs) (not kg), and L is the quantity of Light-ale beer (in kegs) The prices that can be charged are determined by supply and demand forces and are influenced by the quantities of each type according to the following equations: PD=53-D + L for the price $/keg for Dark-ale beer PL= = 42 + 2D - L for the price $/keg for Light-ale beer The total revenue is given by the equation: TR = PD X D + P₁ X L And the profit given by the equation: Profit = TR - TC (a) Write down the profit in terms of D and L only. (b) The total production (quantity) of both beers combined is restricted to 191 kegs. Formulate th
Microeconomics: Private and Public Choice (MindTap Course List)
16th Edition
ISBN:9781305506893
Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Publisher:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Chapter11: Price-searcher Markets With High Entry Barriers
Section: Chapter Questions
Problem 14CQ
Related questions
Question
![A boutique beer brewery produces 2 types of beers, Dark-ale and Light-ale daily with a total cost
function given by
TC = 8D + D XL+ 3L
where D is the quantity of Dark-ale beer (in kegs) (not kg), and
L is the quantity of Light-ale beer (in kegs)
The prices that can be charged are determined by supply and demand forces and are influenced by
the quantities of each type according to the following equations:
PD=53-D + L for the price $/keg for Dark-ale beer
PL = 42 + 2D-L for the price $/keg for Light-ale beer
The total revenue is given by the equation: TR = PD X D + P₁ x L
And the profit given by the equation: Profit = TR - TC
(a) Write down the profit in terms of D and L only.
(b) The total production (quantity) of both beers combined is restricted to 191 kegs. Formulate the
problem using the method of Lagrange multipliers. Find the maximum profit for the appropriate
values of D and L. Note that they need not be whole numbers.
Note that to get full marks, you need to check that the optimal point is a maximum, not minimum.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F655677cc-c92a-473f-8763-0c102c28a775%2F2787d365-9761-4d33-b695-3fbfb27edb53%2Fr54uf5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A boutique beer brewery produces 2 types of beers, Dark-ale and Light-ale daily with a total cost
function given by
TC = 8D + D XL+ 3L
where D is the quantity of Dark-ale beer (in kegs) (not kg), and
L is the quantity of Light-ale beer (in kegs)
The prices that can be charged are determined by supply and demand forces and are influenced by
the quantities of each type according to the following equations:
PD=53-D + L for the price $/keg for Dark-ale beer
PL = 42 + 2D-L for the price $/keg for Light-ale beer
The total revenue is given by the equation: TR = PD X D + P₁ x L
And the profit given by the equation: Profit = TR - TC
(a) Write down the profit in terms of D and L only.
(b) The total production (quantity) of both beers combined is restricted to 191 kegs. Formulate the
problem using the method of Lagrange multipliers. Find the maximum profit for the appropriate
values of D and L. Note that they need not be whole numbers.
Note that to get full marks, you need to check that the optimal point is a maximum, not minimum.
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