Minimise Z=∑_ j=1 ^ n ∑_ i=1 ^ m c_ i j x_ i j Subject to ∑_ i=1 ^ m x_ i j =b_ j , j=1,2, , n∑_ j=1 ^ n x_ i j =b_ j , i=1,2, , m is a L P P with number of constr

Correct answer: C. m+n Constraints will be x_ 11 +x_ 21 + .+x_ ml =b_ 1 x_ 12 +x_ 22 + x_ m 2 =b_ 2 x_ +x_ 2 n + .+x_ mn =b_ n x_ 11 +x_ 12 + +x_ 1 n =b_ 1 x_ 21 +x_ 22 + +x_ 2 n =b_ 2 x_ ml +x_ m 2 + +x_ mn =b_ n So, total number of constraints =m+n

BITSAT 2015

Exam: BITSAT
Year: 2015
Subject: Mathematics
Chapter: Linear Programming

BITSAT 2015 · Mathematics · Linear Programming

Minimise Z=∑_ j=1 ^ n ∑_ i=1 ^ m c_ i j x_ i j Subject to ∑_ i=1 ^...

Minimise

Z=\sum_{j=1}^{n} \sum_{i=1}^{m} c_{i j} x_{i j}

Subject to

\sum_{i=1}^{m} x_{i j}=b_{j}, j=1,2, \ldots, n\sum_{j=1}^{n} x_{i j}=b_{j}, i=1,2, \ldots, m

is a

L P P

with number of constr

Options

A $m-n$
B $m$
C $\mathrm{m}+\mathrm{n}$
D $\frac{\mathrm{m}}{\mathrm{n}}$

Correct answer

C. $\mathrm{m}+\mathrm{n}$

Step-by-step solution

Constraints will be

\mathrm{x}_{11}+\mathrm{x}_{21}+\ldots.+\mathrm{x}_{\mathrm{ml}}=\mathrm{b}_{1} \mathrm{x}_{12}+\mathrm{x}_{22}+\ldots \ldots \mathrm{x}_{\mathrm{m} 2}=\mathrm{b}_{2}\mathrm{x}_{\ln }+\mathrm{x}_{2 \mathrm{n}}+\ldots.+\mathrm{x}_{\mathrm{mn}}=\mathrm{b}_{\mathrm{n}}\mathrm{x}_{11}+\mathrm{x}_{12}+\ldots+\mathrm{x}_{1 \mathrm{n}}=\mathrm{b}_{1}\mathrm{x}_{21}+\mathrm{x}_{22}+\ldots+\mathrm{x}_{2 \mathrm{n}}=\mathrm{b}_{2}\mathrm{x}_{\mathrm{ml}}+\mathrm{x}_{\mathrm{m} 2}+\ldots+\mathrm{x}_{\mathrm{mn}}=\mathrm{b}_{\mathrm{n}}

So, total number of constraints

=\mathrm{m}+\mathrm{n}

Practice Linear Programming on Quantrex Academy →

More from Linear Programming

If the number of available constraints is 3 and the number of parameters to be optimise… BITSAT 2024 Minimum value of Z=3 x+5 y subject to constraints x+y ≥ 2, x+3 y ≥ 3, x, y ≥ 0 BITSAT 2023 The maximum value of z=5 x+2 y subject to constraints x+y ≤ 7, x+2 y ≤ 10, x, y ≥ 0 BITSAT 2023 The maximum value of z=6 x+8 y subject to constraints 2 x+y ≤ 30, x+2 y ≤ 24 and x ≥ 0, y… BITSAT 2020 The maximum value of Z = 4x + 2y subject to constraints 2x + 3y ≤ 18, x + y ≥ 10 and x, y… BITSAT 2018 The coordinates of the point at which minimum value of Z = 7x - 8y subject to constraints… BITSAT 2018 Consider (x)/(2)+(y)/(4) ≥ 1 and (x)/(3)+(y)/(2) ≤ 1, x, y ≥ 0 . Then number of possible… BITSAT 2014 A shopkeeper wants to purchase two articles A and B of t price 4 and 3 respectively. He… BITSAT 2013 Which of the following is not a vertex of the positive region bounded by the inqualities… BITSAT 2011 For the constraints of a L.P. Problem given by x_1+2 x_2 ≤ 2000, x_1+x_2 ≤ 1500 and x_2 ≤… BITSAT 2011 Full Linear Programming list Linear Programming JEE Maths PYQs JEE Mathematics PYQs All BITSAT PYQs