A soda bottling plant uses are capital (K), electricity (E) and raw materials (R) in production. Its production technology can be represented by the following function: Q(R, E, K) = R1/3 E²/3 + K where, Q is the number of bottles produced. The capital used in production is fixed at any point in time because it uses a fully automating assembly line production. The plant can only vary the quantity of raw materials and electricity to adjust output or costs. The hourly cost of raw materials (p) is $10 and the hourly rate of energy (h) is $12. The total hourly cost of capital is $100. The marginal productivities of R and E are as follows: 1 MPR =R-2/3 E²/3 , MPE = 2R/³E-1/3 R/3E-1/3 vi) What is the maximum hourly output the plant can produce if K=30? A.) Q= 10.06 B.) Q= 7.02 C.) Q= 37.02 D.) Q= 17.67
A soda bottling plant uses are capital (K), electricity (E) and raw materials (R) in production. Its production technology can be represented by the following function: Q(R, E, K) = R1/3 E²/3 + K where, Q is the number of bottles produced. The capital used in production is fixed at any point in time because it uses a fully automating assembly line production. The plant can only vary the quantity of raw materials and electricity to adjust output or costs. The hourly cost of raw materials (p) is $10 and the hourly rate of energy (h) is $12. The total hourly cost of capital is $100. The marginal productivities of R and E are as follows: 1 MPR =R-2/3 E²/3 , MPE = 2R/³E-1/3 R/3E-1/3 vi) What is the maximum hourly output the plant can produce if K=30? A.) Q= 10.06 B.) Q= 7.02 C.) Q= 37.02 D.) Q= 17.67
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter8: Cost Analysis
Section: Chapter Questions
Problem 5E
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![A soda bottling plant uses are capital (K), electricity (E) and raw materials (R) in production. Its
production technology can be represented by the following function:
Q(R, E, K) = R/³ E²/3 + K
where, Q is the number of bottles produced. The capital used in production is fixed at any point in
time because it uses a fully automating assembly line production. The plant can only vary the
quantity of raw materials and electricity to adjust output or costs. The hourly cost of raw materials
(p) is $10 and the hourly rate of energy (h) is $12. The total hourly cost of capital is $100. The
marginal productivities of R and E are as follows:
1
MPR = R-2/3 E2/3, MPE =R!/3 E-1/3
vi) What is the maximum hourly output the plant can produce if K=30?
A.) Q= 10.06
B.) Q= 7.02
C.) Q= 37.02
D.) Q= 17.67](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2aa5be87-399a-40b3-98ac-1c02e916530c%2F19e4e72f-ebf9-4de8-958f-1a14af9483ec%2Fqjz7akg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A soda bottling plant uses are capital (K), electricity (E) and raw materials (R) in production. Its
production technology can be represented by the following function:
Q(R, E, K) = R/³ E²/3 + K
where, Q is the number of bottles produced. The capital used in production is fixed at any point in
time because it uses a fully automating assembly line production. The plant can only vary the
quantity of raw materials and electricity to adjust output or costs. The hourly cost of raw materials
(p) is $10 and the hourly rate of energy (h) is $12. The total hourly cost of capital is $100. The
marginal productivities of R and E are as follows:
1
MPR = R-2/3 E2/3, MPE =R!/3 E-1/3
vi) What is the maximum hourly output the plant can produce if K=30?
A.) Q= 10.06
B.) Q= 7.02
C.) Q= 37.02
D.) Q= 17.67
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