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Question: (a) A firm uses capital K, labour L, and land T to produce Q units of a commodity, where
Q = K2/3 + L1/2 + T1/3
Suppose that the firm is paid a positive price p for each unit it produces, and that the positive prices it pays per unit of capital, labour, and land are r, w, and q, respectively. Express the firm's profits as a function π of (K, L, T ), then find the values of K, L, and T (as functions of the four prices) that maximize the firm's profits (assuming a maximum exists).
(b) Let Q∗ denote the optimal number of units produced and K∗ the optimal capital stock. Show that ∂Q∗/∂r = -∂K∗/∂p.
Let S be the part of the plane 2x+2y+z=2 which lies in the first octant, oriented upward. Find the flux of the vector field F=4i+1j+2k across the surface S.
A 52 foot building casts a shadow that is 48 feet long. At the same time, the shadow cast by a nearby statue is 18 feet long. How tall is the statue?
How many different bit strings can be transmitted if the string must begin with a 1 bit, must include three additional 1 bits (so that a total of four 1 bits is sent), must include a total of 12 0 bits, and must have at least two 0 bits following ..
SPORTS In the men's tennis tournament at Wimbledon, two finalists, A and B, are competing for the title, which will be awarded to the first player.
The sum of 3 consecutive ODD integers is 189. What is the first integer? (Be sure to type only the first integer in the answer blank. Do not use any variables or words.)
Find the center of mass of the solid bounded by the graphs of x2 + y2 + z2 = 4 and x2 + y2 = 2y if the density is proportional to the distance from the xy plane
Find the magnitude of the resultant force and the angle it makes with the positive x-axis. (Let a = 100 N and b = 500 N. Round your answers to one decimal plaand amgle itce.)
Given: ABCD is a trapezoid. ΔAYD is congruent to ΔBCY. ABYD is a rhombus. AD=3 and AX=1. Find the length of all sides and diagonals.
Calculate the standard deviation
Find the Maclaurin polynomial Tn.x/ (for a general n) for the function f .x/ D 2x.
A common misconception is that if A has a strictly dominant eigenvalue, then, for any sufficiently large value of k, the vector Akx is approximately equal.
you are going to roll four twenty-sided dice. if the rolls total to 20 or less roll two more twenty-sided dice and add
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