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Home » Refer to Exercise 15. Determine the maximum distance that the man can travel.
Refer to Exercise 15. Determine the maximum distance that the man can travel.
CBSE | Class 12 | Exercise 1 | Linear Programming | Maths | NCERT Exemplar
Refer to Exercise 15. Determine the maximum distance that the man can travel.

As per the solution of exercise 15, we have

Maximize Z = x + y, subject to the constraints

    \[2x\text{ }+\text{ }3y\le 120\]

… (i)

    \[8x\text{ }+\text{ }5y\le 400\]

… (ii)

    \[x\ge 0,\text{ }y\ge 0\]

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

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

    \[x\text{ }=\text{ }300/7\text{ }and\text{ }y\text{ }=\text{ }80/7\]

It’s seen that the feasible region whose corner points are

    \[O\left( 0,\text{ }0 \right),\text{ }A\left( 50,\text{ }0 \right),\text{ }B\left( 300/7,\text{ }80/7 \right)\text{ }and\text{ }C\left( 0,\text{ }40 \right)\]

.

Let’s evaluate the value of Z

From above table the maximum value of Z is

    \[54.3\]

Therefore, the maximum distance that the man can travel is

    \[54.3\]

km at

    \[(300/7,80/7)\]

.

i

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