The daily output at a plant manufacturing desks is approximated by the function f(L,K)=30K7/10L4/5 desks 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 $14,000 and the average wage of an employee is $11.50 per hour, what combination of worker-hours (to the nearest hundred) and capital expenditures (to the nearest thousand) will yield maximum daily production?

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batolisis batolisis · Answer 1 · 2021-05-05T14:24:00+02:00

Answer: Hello your function is poorly written below is the properly written function f( L,K ) = 30K^(7/10) L^(4/5)

answer : K = $7000 , L = 600 hours

Explanation:

Given Function = f( L,K ) = 30K^(7/10) L^(4/5)

L = size of labor in workers-hours

K = daily capital investment

Daily budget = $14000

average wage of employee = $11.5

Determine the combinations and capital expenditure that would yield max daily production

we will apply the relation below

K^(7/10) = L^(4/5)

K^(7/10) ≈ L^(8/10) ( where L = 14000 - k )

K^(7/10) = ( 14000 - k )^(8/10 )

when we resolve the above equation

K = $7000

L = 7000 / 11.5 ≈ 608 workers