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Refer to Exercise 12. What will be the minimum cost?
CBSE | Class 12 | Exercise 1 | Linear Programming | Maths | NCERT Exemplar
Refer to Exercise 12. What will be the minimum cost?

As per the solution of exercise 12, we have

The objective function for minimum cost is

    \[Z\text{ }=\text{ }400x\text{ }+\text{ }200y\]

Subject to the constrains;

    \[5x\text{ }+\text{ }2y\ge 30\]

….. (i)

    \[2x\text{ }+\text{ }y\le 15\]

….. (ii)

    \[x\le y\]

…. (iii)

and

    \[x\ge 0,\text{ }y\ge 0\]

(non-negative constraints)

Now, let’s construct a constrain table for the above

Next, solving equations (i) and (iii), we get

    \[x\text{ }=\text{ }30/7\text{ }and\text{ }y\text{ }=\text{ }30/7\]

, so the corner point is

    \[A\left( 30/7,\text{ }30/7 \right)\]

On solving equations (ii) and (iii), we get

    \[x\text{ }=\text{ }5\text{ }and\text{ }y\text{ }=\text{ }5\]

, so the corner point is

    \[B(5,5)\]

Here, ABC is the shaded feasible region whose corner points are

    \[A\left( 30/7,\text{ }30/7 \right),\text{ }B\left( 5,\text{ }5 \right)\text{ }and\text{ }C\left( 0,\text{ }15 \right)\]

On evaluating the value of Z, we have

From the table it’s seen that the minimum value is

    \[2571.4\]

Therefore, the required minimum cost is Rs

    \[2571.4\]

at

    \[(30/7,30/7)\]

i

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