Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
Complete Question
The daily output at a plant manufacturing chairs is approximated by the function
[tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex] chairs
where L is the size of the labor force measured in hundreds
of worker-hours and K is the daily capital investment in thousands of dollars. If the plant manager has a daily budget of $13,000 and the average wage of an employee is $9.00 per hour, what combination of worker-hours (to the nearest hundred) and capital expenditures (to the nearest thousand) will yield maximum daily production?
a)200 worker-hours and $9000 in capital expenditure
b)1100 worker-hours and $3000 in capital expenditure
c)500 worker-hours and $8000 in capital expenditure
d)900 worker-hours and $5000 in capital expenditure
e)600 worker-hours and $6000 in capital expenditure
f)300 worker-hours and $10,000 in capital expenditure
Answer:
d)900 worker-hours and $5000 in capital expenditure
Step-by-step explanation:
From the question we are told that
Daily output at a plant manufacturing chairs is approximated by the function [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex]
Daily budget of $13,000
Average wage of an employee is $9.00 per hour
a) Generally the function [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex] can be use to for (a)
Mathematically solving with L=200 K=9000
[tex]f(L=200,K=9000) = (45\sqrt[3]{9000})200^3^/^5[/tex]
[tex]f(L=200,K=9000) = 45*20.8*24[/tex]
[tex]f(L=200,K=9000) = 22464[/tex]
b)Generally the function [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex] can be use to for (b)
Mathematically solving with L=1100 K=3000
[tex]f(L=1100,K=3000) = (45\sqrt[3]{3000})1100^3^/^5[/tex]
[tex]f(L=1100,K=3000) = 45*14.4*66.8[/tex]
[tex]f(L=1100,K=3000) = 43286.4[/tex]
c)Generally the function [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex] can be use to find (c)
Mathematically solving with L=500 K=8000
[tex]f(L=500,K=8000) = (45*\sqrt[3]{8000})*500^3^/^5[/tex]
[tex]f(L=500,K=8000) = 45*20*41.63[/tex]
[tex]f(L=500,K=8000) =37467[/tex]
d)Generally the function [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex] can be use to find (d)
Mathematically solving with L=900 K=5000
[tex]f(L=900,K=5000) = (45*\sqrt[3]{5000})*900^3^/^5[/tex]
[tex]f(L=900,K=5000) = 45*17.09*59.2[/tex]
[tex]f(L=900,K=5000) =45577.88[/tex]
e)Generally the function [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex] can be use to find (e)
Mathematically solving with L=600 K=6000
[tex]f(L=600,K=6000) = (45\sqrt[3]{6000})600^3^/^5[/tex]
[tex]f(L=600,K=6000) = 45*18.17*46.4[/tex]
[tex]f(L=600,K=6000) =37974[/tex]
f)Generally the function [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex] can be use to find (e)
Mathematically solving with L=600 K=6000
[tex]f(L=300,K=10,000) = (45*\sqrt[3]{10,000})*300^3^/^5[/tex]
[tex]f(L=300,K=10,000) = 45*21.5*30.6[/tex]
[tex]f(L=300,K=10,000) = 29704.2[/tex]
Therefore the function f shows maximum at L=900 K=5000
Giving the correct answer to be
d)900 worker-hours and $5000 in capital expenditure
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
