Customers buy 11 units of regular beer and 17 units of light beer monthly. The brewery decides to produce extra beer, beyond that needed to satisfy the customers. The cost per unit of regular beer is $33,000 and the cost per unit of light beer is $48,000. Every unit of regular beer brings in $200,000 in revenue, while every unit of light beer brings in $400,000 in revenue. The brewery wants at least $20,000,000 in revenue. At least 47 additional units of beer can be sold. Complete parts (a) and (b). (a) How much of each type of beer should be made so as to minimize total production costs? Let y₁ represent units of regular beer and y₂ represent units of light beer. Find the objective function, w, used to minimize production costs. w=y₁ + ₁+ y₂ (Do not include the $ symbol in your answers.) The brewery should make units of regular beer and (Simplify your answers.) What is the minimum cost? units of light beer so as to minimize total production costs. The minimum cost is $ (Simplify your answer. Round to the nearest thousand as needed.) (b) Suppose the minimum revenue is increased to $20,200,000. Use shadow costs to calculate the new total production costs. (Simplify your answer. Round to the nearest thousand as needed.)
Customers buy 11 units of regular beer and 17 units of light beer monthly. The brewery decides to produce extra beer, beyond that needed to satisfy the customers. The cost per unit of regular beer is $33,000 and the cost per unit of light beer is $48,000. Every unit of regular beer brings in $200,000 in revenue, while every unit of light beer brings in $400,000 in revenue. The brewery wants at least $20,000,000 in revenue. At least 47 additional units of beer can be sold. Complete parts (a) and (b). (a) How much of each type of beer should be made so as to minimize total production costs? Let y₁ represent units of regular beer and y₂ represent units of light beer. Find the objective function, w, used to minimize production costs. w=y₁ + ₁+ y₂ (Do not include the $ symbol in your answers.) The brewery should make units of regular beer and (Simplify your answers.) What is the minimum cost? units of light beer so as to minimize total production costs. The minimum cost is $ (Simplify your answer. Round to the nearest thousand as needed.) (b) Suppose the minimum revenue is increased to $20,200,000. Use shadow costs to calculate the new total production costs. (Simplify your answer. Round to the nearest thousand as needed.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Customers buy 11 units of regular beer and 17 units of light beer monthly. The brewery decides to produce extra beer, beyond that needed to satisfy the customers. The cost per unit of regular beer
is $33,000 and the cost per unit of light beer is $48,000. Every unit of regular beer brings in $200,000 in revenue, while every unit of light beer brings in $400,000 in revenue. The brewery wants at
least $20,000,000 in revenue. At least 47 additional units of beer can be sold. Complete parts (a) and (b).
(a) How much of each type of beer should be made so as to minimize total production costs?
Let y₁ represent units of regular beer and y₂ represent units of light beer. Find the objective function, w, used to minimize production costs.
w = y₁ + y₂
(Do not include the $ symbol in your answers.)
The brewery should make units of regular beer and
(Simplify your answers.)
What is the minimum cost?
units of light beer so as to minimize total production costs.
The minimum cost is $
(Simplify your answer. Round to the nearest thousand as needed.)
(b) Suppose the minimum revenue is increased to $20,200,000. Use shadow costs to calculate the new total production costs.
(Simplify your answer. Round to the nearest thousand as needed.)
$
891439
1898:938
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Customer buy 11 units of regular beer and 17units of light beer monthly,
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