The production function for a competitive firm is Q = K.5L.5. The firm sells its output at a price of
$10, and can hire labor at a wage of $5. Capital is fixed at one unit. The profit-maximizing
quantity of labor is:
A. 2/5.
B. 1.
C. 10.
D. None of the answers are correct.

please explain in details

Suppose life expectancy in years (l) is a function of two inputs, health expenditures (h) and nutrition expenditures (n) in hundreds of dollars per year. the production function is upper l equals ch superscript 0.40 baseline upper n superscript 0.60l=ch0.40n0.60. beginning with c = 1, a health input of $400400 per year (hequals=44) and a nutrition input of $400400 per year (nequals=44), show that the marginal product of health expenditures and the marginal product of nutrition expenditures are both decreasing. the marginal product of health expenditures when h goes from 44 to 55 is nothing, and the marginal product of health when h goes from 66 to 77 is nothing. (round your answers to three decimal places.)

scenario: hawaii and south carolina are trading partners. hawaii has an absolute advantage in the production of both coffee and tea. the opportunity cost of producing 1 pound of tea in hawaii is 2 pounds of coffee, and the opportunity cost of producing 1 pound of tea in south carolina is 1/3 pound of coffee. which of the following statements is true? a. south carolina should specialize in the production of both tea and coffee. b. hawaii should specialize in the production of tea, whereas south carolina should specialize in the production of coffee. c. hawaii should specialize in the production of coffee, whereas south carolina should specialize in the production of tea. d. hawaii should specialize in the production of both tea and coffee.

Miller company’s total sales are $171,000. the company’s direct labor cost is $20,520, which represents 30% of its total conversion cost and 40% of its total prime cost. its total selling and administrative expense is $25,650 and its only variable selling and administrative expense is a sales commission of 5% of sales. the company maintains no beginning or ending inventories and its manufacturing overhead costs are entirely fixed costs. required: 1. what is the total manufacturing overhead cost? 2. what is the total direct materials cost? 3. what is the total manufacturing cost? 4. what is the total variable selling and administrative cost? 5. what is the total variable cost? 6. what is the total fixed cost? 7. what is the total contribution margin?