The corner points of the feasible region determined by the system of linear constraints are 0-0-0-40-20-40-60-20-60-0- The objective function is Z -4 x -3 y- Compare the quantity in column A and column B-Wheend array a The qunatity in column A is greaterb The qunatity in column b is greaterc The two quantities are equald The relationship cannot be determined on the basis of the information supplied-

[ Corner points amp; Corrsponding vlaue of; amp; Z=4x+3y; (0,0) a ...

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Standard XII

Mathematics

Graphical Method of Solving Linear Programming Problems

The corner po...

Question

The corner points of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20), (60, 0). The objective function is Z = 4x + 3y. Compare the quantity in column A and column B.

$\begin{matrix} Column A & Column B Maximum of Z & 325 \end{matrix}$
(a) The qunatity in column A is greater
(b) The qunatity in column b is greater
(c) The two quantities are equal
(d) The relationship cannot be determined on the basis of the information supplied.

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Solution

$\begin{matrix} Corner points & Corrsponding vlaue of Z=4x+3y (0, 0) & 0 (0, 40) & 120 (20, 40) & 200 (60, 20) & 300 \leftarrow M a x i m u m (60, 0) & 240 \end{matrix}$
Hence, maximum value of Z =300 < 325
So, the quantity in column B is greater.

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Q. The corner points of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20), (60, 0). The objective function is z = 4x + 3y.
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Corner pointsCorrsponding vlaue ofZ=4x+3y(0,0)0(0,40)120(20,40)200(60,20)300←Maximum(60,0)240 Hence, maximum value of Z =300 < 325 So, the quantity in column B is greater.

$\begin{matrix} Corner points & Corrsponding vlaue of Z=4x+3y (0, 0) & 0 (0, 40) & 120 (20, 40) & 200 (60, 20) & 300 \leftarrow M a x i m u m (60, 0) & 240 \end{matrix}$
Hence, maximum value of Z =300 < 325
So, the quantity in column B is greater.