Question 3: A firm's production function is given by Q = L2VK + 2LK? with K = 16 andL = 10.a) Find the value of the marginal product of capital, M PK and the value of the marginal productof labour, MPL-b) Write down the value of the marginal rate of technical substitution, MRTS and give aninterpretation of this value.c) Estimate the overall effect on Q when K increases by 2 units and L decreases by 3 units.

production function of a firm is defined as Q=L2K+2LK2 with K=16 , L=10 (a) find the value of the…

Answered: Question 3: A firm's production…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A weather balloon that contains 540 m3 of helium springs a leak and empties in 60 seconds. Suppose that the volume of helium in the balloon as a function of time is given by V (t)= 540(1-t/60)^3. Find (a) the average rate of change of volume during the 60 seconds it takes to empty. b) the volume of the balloon after 40 seconds. c) the instantaneous rate of change of the volume at 40 seconds.
12. A rectangular tank measuring 1 m × 2 m × 3 m initially contains water up to a height of 1 m. Water is being pumped into the tank at a rate of 40 L/min while simultaneously being drained at a rate of 20 L/min. (Hint: 1m³ = 1000L.) (a) How many minutes will it take to fill the tank? (b) What is the rate of change of the height of the water in the tank in m/min?
17. Trepy Bros, has been doing business for a very long time. The board has assessed the gross yearly income after t a long time to be V(10t2 +t + 236) in large number of dollars. What was the yearly pace of development of income following four years? As a rate, what was the pace of development of the profit following four years?
5. Suppose that sodium pentobarbital is used to anesthetize a dog. The dog is anesthetized when its bloodstream contains at least 45 milligrams (mg) of sodium pentobarbitol per kilogram of the dog's body weight. Suppose also that sodium pentobarbitol is eliminated from the dog's bloodstream at a rate which is proportional to the amount of sodium pentobarbitol in the bloodstream and that after 5 hours half of the initially prescribed sodium pentobarbitol is elliminated from the bloodstream. Set up and solve an initial value differential equation. What single dose should be administered in order to anesthetize a 50-kg dog for 1 hr?
The total profit in thousands of dollars, for a product is given by (see attachment) and x is the number of units produced. Determine the marginal profit function when x=15.

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