The daily output at a plant manufacturing toasters is approximated by the function f(L,K)=20K^4/5 L^9/10 toasters 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 $21,000 and the average wage of an employee is $7.00 per hour, what combination of worker-hours (to the nearest hundred) and capital expenditures (to the nearest thousand) will yield maximum daily production? a) 500 worker-hours and $18,000 in capital expenditures b) 2100 worker-hours and $9,000 in capital expenditures c) 1600 worker-hours and $10,000 in capital expenditures d) 700 worker-hours and $16,000 in capital expenditures e) 800 worker-hours and $15,000 in capital expenditures f) 1000 worker-hours and $16,000 in capital expenditures

The combination of worker-hours and capital expenditures that will yield maximum daily production is e) 800 worker-hours and $15,000 in capital expenditures.

To find the combination that maximizes daily production, we need to maximize the function f(L, K) = 20K^4/5 L^9/10 given the budget constraints. The budget constraint in this case is $21,000.

To convert the budget constraint into worker-hours and capital expenditures, we need to consider the average wage of $7.00 per hour. The total available worker-hours can be calculated by dividing the budget by the wage: $21,000 / $7.00 = 3,000 worker-hours.

Now we can compare the available worker-hours with the options provided:

a) 500 worker-hours: Not enough worker-hours.

b) 2100 worker-hours: Within the available worker-hours but not the best option.

c) 1600 worker-hours: Within the available worker-hours but not the best option.

d) 700 worker-hours: Not enough worker-hours.

e) 800 worker-hours: Within the available worker-hours and a potential candidate.

f) 1000 worker-hours: Within the available worker-hours but not the best option.

Now let's consider the capital expenditures:

a) $18,000: Within the budget.

b) $9,000: Within the budget but not the best option.

c) $10,000: Within the budget and a potential candidate.

d) $16,000: Within the budget but not the best option.

e) $15,000: Within the budget and a potential candidate.

f) $16,000: Within the budget but not the best option.

Considering both worker-hours and capital expenditures, the combination that maximizes daily production is e) 800 worker-hours and $15,000 in capital expenditures.

Learn more about capital expenditures.
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