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A manufacture of tricycle parts sells three tires (x) with each frame (y). The combined cost...

A manufacture of tricycle parts sells three tires (x) with each frame (y). The combined cost function is C = x2 + xy + y2 + 190. The demands for tires and frames are, respectively: x=63–(1/4)Px , and y=60–(1/3)Py .

a) Form the profit function and the Lagrange function.

b) Find the profit maximizing level of output, prices and the value of the Lagrange multiplier.

c) Find the profit for the firm with the output and prices in b.

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Answer #1

Answers a) T = 2520 - 5x²r 180 y - 44²-190 xy Lagrange = 252-44 +180-3y +X (x + xy + y² 190) b) n=25.52 y = 19.31 Px. = 149.9The combined Cost function in C =X2 + xyty2 +190 demands X = 63- ( Px ² Yulx = 63-x. y = 60 - YPY A P = 63x4 - 4x x = 252-40Second Order Condition Пух = -10 Tyy = af Tay=-1 differentiating The with o respect to a Similarly for y for Thay, differentiU(x,y) - f(x) +7 (1) L = as) - чи igo -3ч х( 449 L - -ч +21 + 2 =o - -ч +(ax ty) = Су: -3 + * + 29, 2ə - - 3 + (2х)- Lл - меч

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