The production function for a firm is p(x, y) = 96x`3/4 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.(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 – 96x3/4 1/4= 0.x= 625 , y= 16 (Type exact answers in simplified form.)(b) Find the value of A at the optimal level of production.(Type an exact answer in simplified form.)

P(x,y)=96x34.y14 Labor cost =$144 Capital cost =$1875 cost =144x+1875y

Answered: The production function for a firm is…

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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