The daily output at a plant manufacturing transistor radios is approximated by the function radios, where L is the size of the labor force measured in hundreds of worker hours and K is the capital investment in thousands of dollars. Suppose the plant manager has a daily budget of $18,000 to be invested in capital or spent on labor and that the average wage of an employee at the radio plant is $7.00 per hour. What combination of worker hours and capital expenditures will yield the maximum daily production? Round your answers to the nearest integer.
A) labor-hours
B) labor-hours
C) labor-hours
D) labor-hours
E) labor-hours

Question

The daily output at a plant manufacturing transistor radios is approximated by the function  radios, where L is the size of the labor force measured in hundreds of worker hours and K is the capital investment in thousands of dollars. Suppose the plant manager has a daily budget of $18,000 to be invested in capital or spent on labor and that the average wage of an employee at the radio plant is $7.00 per hour. What combination of worker hours and capital expenditures will yield the maximum daily production? Round your answers to the nearest integer.
A) labor-hours 
B) labor-hours 
C) labor-hours 
D) labor-hours 
E) labor-hours

Quizplus · Accepted Answer

We can use the budget constraint to express one variable in terms of the other. Since the wage is $7.00 per hour, we have:
L = 100 * labor-hours = $18,000 / $7.00 per hour = 2,571.43 labor-hours
Thus, we can rewrite the production function as P(K) = 11eaa894_6476_4552_a158_0faea79fdebb_TB6775_11 radios, where K is the capital investment in thousands of dollars. To find the maximum daily production, we need to find the value of K that maximizes P(K).

Taking the derivative of P(K) with respect to K, we get:
P'(K) = 11eaa894_6476_1e45_a158_277bc7a222d6_TB6775_11
Setting this equal to zero and solving for K, we get:
K = 10
Plugging this value of K back into the production function, we get:
P(10) = 11eaa894_6476_bf8e_a158_64cb3ef47c75_TB6775_11 radios
Rounding to the nearest integer, we get:
P(10) ≈ 82 radios

Therefore, the combination of 2,571 labor-hours and $10,000 in capital expenditures will yield the maximum daily production of approximately 82 radios. The correct choice is D.

The Daily Output at a Plant Manufacturing Transistor Radios Is