1. Benefit Cost analysis.Assume a benefit function B = 60*x^.8 and a cost function C = 4 + 7*x^1.5. The maximum difference between B and C are the net benefits. a) Find the value of x that results in the maximum net benefits. b) Would an increase in the fixed cost of 4 affect the value of x? c) Use a Lagrangian model to find the value of the shadow price, or Lagrangian multiplier, if x cannot exceed 5. What does the multiplier signify?
1. Benefit Cost analysis.Assume a benefit function B = 60*x^.8 and a cost function C = 4 + 7*x^1.5. The maximum difference between B and C are the net benefits. a) Find the value of x that results in the maximum net benefits. b) Would an increase in the fixed cost of 4 affect the value of x? c) Use a Lagrangian model to find the value of the shadow price, or Lagrangian multiplier, if x cannot exceed 5. What does the multiplier signify?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 44E
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1. Benefit Cost analysis.Assume a benefit function B = 60*x^.8 and a cost function C = 4 + 7*x^1.5. The maximum difference between B and C are the net benefits.
a) Find the value of x that results in the maximum net benefits.
b) Would an increase in the fixed cost of 4 affect the value of x?
c) Use a Lagrangian model to find the value of the shadow price, or Lagrangian multiplier, if x cannot exceed 5. What does the multiplier signify?
Expert Solution
Step 1
(a) We know that the difference between the benefit function and the cost function is the net benefit.
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