The production function for a firm is p(x, y) = 96x3/4 1/4ywhere x and y are the number of units of labor and capital utilized. Suppose that labor costs $144 per unit and capital costs $1875 per unit and that the firm decides to produce 24,000 units of goods. Determine the following.%3D...3/4 1/4(a) Determine the amounts of labor and capital that should be utilized in order to minimize the cost. That is, find the values of x and y that minimize 144x + 1875y, subject to the constraint 24,000 – 96xy= 0.X =, y=(Type exact answers in simplified form.) The production function for a firm is p(x, y) = 72x3/4 1/4ywhere x and y are the number of units of labor and capital utilized. Suppose that labor costs $108 per unit and capital costs $576 per unit and that the firm decides to produce 9216 units of goods. Determine the following....(a) Determine the amounts of labor and capital that should be utilized in order to minimize the cost. That is, find the values of x and y that minimize 108x + 576y, subject to the constraint 9216 – 72x3/4 1/4= 0.x = 256 , y= 16 (Type exact answers in simplified form.)(b) Find the value of 1 at the optimal level of production.1 = 4 (Type an exact answer in simplified form.)(c) Find the expressions for marginal productivity of labor and marginal productivity of capital. Then find the ratio of marginal productivity of labor to marginal productivity of capital at the optimum level of production and the ratio of unit price of labor to unit price of capital and determine therelationship between the ratios.marginal productivity of labor = 54x– 1/4 1/4ymarginal productivity of capital = 18x3/4 -3/4yDetermine the marginal productivity of labor and marginal productivity of capital at the optimum level of production and then compare the ratios.marginal productivity of labormarginal productivity of capitalunit price of laborunit price of capital331616(Simplify your answers.)

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Answered: roduction function for a firm is p(x,…

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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The demand for ACME Q-bits is given by the function q = f(Y,p), where • q = monthly demand for ACME Q-bits (measured in 1000s of Q-bits) • Y= average monthly income in the Q-bit market (measured in $1000s) •p = price/Q-bit that ACME sets (measured in dollars). When average monthly income is $4500 and ACME's price is $35... • q = 22, aq/əY = 0.77 aq/ap = - 0.64 If average monthly income increases to $4700, by approximately how much can ACME increase their price while keeping demand for the product fixed at q = 22? Hint: Use linear approximation.
The marginal cost to produce one additional (generic consumer good) after having produced a of them already is modeled by C(x) = 3x² 120x + 4800. How many (generic consumer good)s should a company produce to minimize the marginal cost?
The supply function for x thousand units of a product is p = x2 + 2x, dollars per unit. If the equilibrium price is $48 per unit, find the producer’s surplus. Set up an integral, and use your calculator to evaluate it.
You have been placed in charge of minimizing costs on a production line. The cost model is C=100x-12^2+3x^3. The variable x represents the level of production for the given cost. Determine the production level that minimizes the average cost. A.) Find the marginal cost. (Divide by x and take 1st derivative) B.) What is the production level?
If the cost of selling y yards of fabric is given by C (y) = O 10 O _30_j^_^ 2 10 3y 3 2 find an expression for the marginal cost.
Given that a bus can hold up to 60 passengers for a single trip from Town A to Town B. Number of passenger, x per trip is charged with a fare of p Ringgit Malaysia using the equation p = (3 -2. 40 i) Provide an expression for the earning / revenue r(x) per trip received by the bus company. ii) In order to prevent loss in the company, marginal revenue has to be equal to zero. Find the number of people per trip that will make the marginal revenue equal to zero, where marginal revenue is differentiation of r(x) with respect to x.
6 Assume an hypothetical consumer faced by the following utility function; U=X^2Y ( squared times y). After a bad harvest and thus bad economic conditions, the price of good X increases from Ksh.4.2 to Ksh. 4.8, while the price of good Y which was ksh. 4 increased to ksh.5. The income of the consumer was ksh. 30 before and after the good harvest. Calculate the CV and EV.

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