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    Course Name: Level: Ad, Adb, Bs Course Code: 5405 Semester: Spring 2022 Assignment: 2 Due Date: 02-10-2022 Total Assignment: 2 Late Date: 02-10-2022

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    Sikandar Akram
    This document contains an assignment for a mathematics course covering applied mathematics for business and social sciences. The assignment contains 5 questions involving topics like systems of equations, limits, derivatives, and partial derivatives. Students are asked to solve problems, find critical points, maxima/minima, and interpret partial derivatives in an economic context. The due date for the assignment is February 10, 2022.

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    Course Name: Level: Ad, Adb, Bs Course Code: 5405 Semester: Spring 2022 Assignment: 2 Due Date: 02-10-2022 Total Assignment: 2 Late Date: 02-10-2022

    Uploaded by

    Sikandar Akram
    21 views23 pages
    This document contains an assignment for a mathematics course covering applied mathematics for business and social sciences. The assignment contains 5 questions involving topics like systems of equations, limits, derivatives, and partial derivatives. Students are asked to solve problems, find critical points, maxima/minima, and interpret partial derivatives in an economic context. The due date for the assignment is February 10, 2022.

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    5405-2

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    This document contains an assignment for a mathematics course covering applied mathematics for business and social sciences. The assignment contains 5 questions involving topics like systems of equations, limits, derivatives, and partial derivatives. Students are asked to solve problems, find critical points, maxima/minima, and interpret partial derivatives in an economic context. The due date for the assignment is February 10, 2022.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    21 views23 pages

    Course Name: Level: Ad, Adb, Bs Course Code: 5405 Semester: Spring 2022 Assignment: 2 Due Date: 02-10-2022 Total Assignment: 2 Late Date: 02-10-2022

    Uploaded by

    Sikandar Akram
    This document contains an assignment for a mathematics course covering applied mathematics for business and social sciences. The assignment contains 5 questions involving topics like systems of equations, limits, derivatives, and partial derivatives. Students are asked to solve problems, find critical points, maxima/minima, and interpret partial derivatives in an economic context. The due date for the assignment is February 10, 2022.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 23

    www.daniyalstudio9.

    com
    Applied Mathematics
    Course name: for Business & Social Level: AD, ADB, BS
    Sciences
    Course Code: 5405 Semester: Spring 2022
    Assignment: 2 Due Date: 02-10-2022
    Total Assignment: 2 Late Date: 02-10-2022

    ‫اجنےساتکںیبںیہنآریہںیہ۔وہہبلط مہاریرسوسےکذرےعیاسنمنئاوراحتمناتیکیتریےکےیلیک ببرھگےھٹیب‬‫نجہبلطیکویوینریٹسیک ب‬


    ‫ے‬ ‫ٹٹ‬ ‫ے‬
    ‫ادارکےکآرڈررکواتکسںیہ۔زیناہھتےسیھکلوہیئاورالیامیاسییک‬180‫رپنتمیقےکالعوہمزیڈڈاکخزہچ‬
    ‫احلصرکتکسںیہ۔بتکیک ڈ‬
    ‫ئم ٹ‬
    03096696159‫ان‬ ‫وسٹفاس نٹسآرڈررپدایتسبںیہ۔واسٹ پ‬

    Assignment no. 2
    Q. 1
    (a) An economy depends on two basic products, wheat and oil. To produce 1 metric ton of wheat
    requires .25 metric tons of wheat and .33 metric tons of oil. Production of 1 metric ton of oil consumes
    .08 metric tons of wheat and .11 metric tons of oil. Find the production that will satisfy a demand of
    500 metric tons of wheat and 1000 metric tons of oil.

    m n  x y  t s 
    (b) Given the matrices: P =  , X =  , T =  . Verify the following statements:
     p q   z w t u 
    i) (PX)T = P(XT) (Associative Property)
    PX(T) =
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    P(XT)=

    ii) P(X + T) = PX + PT (Distributive Property)


    P(X + T) =

    PX + PT =
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    PX + PT =

    Q. 2

    (a) Determine the inverse of by using the matrix of cofactor approach.


    www.daniyalstudio9.com

    (b) Solve the given system of equations by using Cramer’s rule.


    www.daniyalstudio9.com
    x1 – 4x2 + x3 = 12
    7x1 –6x3 = 18
    2x2 + 5x3 = 7
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    www.daniyalstudio9.com

    Q. 3
    (a) Find the following limits:

    i) lim x→3 x 2 − 5

    x− 8
    ii) lim x→8
    x −8
    www.daniyalstudio9.com

    3x
    iii) lim x→−2
    ( x + 2) 3

    (b) Living standards are defined by the total output of goods and services divided by the total
    population. In the United States during the 1980s, living standards were closely approximated by
    f ( x) = −.023x 3 + 0.3x 2 − 0.4 x + 11.6
    Where x=0 corresponds to 1981. Find the derivative of f. Use the derivative to find the rate of change
    in living standards in the following years.
    1.1981
    f ( x) = −.023x 3 + 0.3x 2 − 0.4 x + 11.6
    x=0
    f(x) = 11.6
    2.1988
    f’(x) =
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    x=0
    f’(x) = -0.4
    3.1989
    f’’(x)

    x=0
    f’’(x) = 0.6

    4.1990
    f’’’(x) = - 69 /500 = -0.138
    5.What do your answers to part (i) – (iv) tell you about living standards in those years?
    From above result, 1981 is best for living standards.
    Q. 4
    (a) Find critical points of the given functions. Use second derivate test on each critical point to
    determine whether it leads to a relative maximum or minimum.
    f(x) = x4, –32x2 + 7
    www.daniyalstudio9.com

    (b) Determine the location and values of the absolute maximum and absolute minimum for the given
    function.
    f(x) = (–x + 2)4, where 0  x  3
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    www.daniyalstudio9.com

    Q. 5
    (a) Find fx , fy , fz , fyx , fxz , fzy , fy , (2, –1, 3), fyz, (–1, 1, 0). if
    2 x 2 + xy
    f(x, y, z) =
    yz − 2
    fx =
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    fy =
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    fz =
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    fyz =
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    fyx =
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    fzy =
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    (b) Suppose z = f (x, y) describes the cost to build a certain structure, where x represents the labor
    costs and y represents the cost of materials. Describe what fx and fy represent.
    Basically fx and fy represents the marginal labour cost and marginal cost of materials respectively. fx and
    fy are calculated by taking partial derivatives of z.

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