Cola War

In: Business and Management

Submitted By jimmylosel
Words 567
Pages 3
BMS 101: BUSINESS MATHEMATICS
COMMON FOUNDATION
Assignment on
-------------------------------------------------
PARTIAL DIFFERENTIATION
1. Find the first order derivatives of the following functions: i. fx,y=xex2-y2 ii. fx,y=exy
2. If z=x2fyx, show that x∂z∂x +y∂z∂y =2z.
3. Find all the second-order partial derivatives of the following functions. (i) z= y2ex+logxy (ii) z= logx2y4
4. (i). If z=fx+ay+gx-ay, Show that ∂2z∂y2= a2∂2z∂x2.
(ii). If z=logx3+y3x2+y2, prove that x∂z∂x +y∂z∂y =1
5. Show that each of the following function is homogeneous of degree of 1. (i) fx,y= ax-β+ by-β-1β
6. If z=axαyβ, verify that (i) x2∂2z∂x2+2xy∂2z∂x∂y+y2∂2z∂y2=α+βα+β-1 z

7. Verify Euler’s theorem for (i) z=x3+y3xy (ii) z=logyx
8. Examine the following functions for relative maximum or minimum: (i) z=fx,y=x2+3y2+4x-9y+3. (ii) z=fx,y=2xy-2x2-y2-8x+6y+4.
9. The demand functions of two commodities X1and X2 are given as x1=1000+200p1+2-20p2 and x2=1000+500p1+4-50p2
(i). Find the four partial marginal demand functions and determine whether the commodities are competitive or complementary.
(ii). Calculate the four partial Elasticities of demand at p1=3 and p1=1.
10. The demand functions for two commodities X1and X2 are each a function of the prices of X1and X2 and are given by x1=4p12p2 and x2=16p1p22 respectively. Find the four partial marginal demand functions and determine whether X1and X2 are competitive, complementary or neither. Also determine the four partial Elasticities of demand.
11. For the production function Q=fL,K given implicitly, in the form FL,K,Q=0, by the equation 6Q3-Q2-6L-24K+L2+4K2+50=0,
Find the marginal productivities…...

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