If Z-5 x-10 y- subject to the constraints x-2 y- 120-x-y- 60-x-2 y- 0 and x- 0- y- 0- then which of the following is-are true -

Z=5 x+10 y subject to the constraints x+2 y≤ 120,x+y≥ 60 ,x 2 y≥ 0 and x≥ 0, y≥ 0 We take the given inequality to find the region bounded by these inequalities. ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Complex Numbers

If Z=5 x+10 y...

Question

If $Z = 5 x + 10 y,$ subject to the constraints $x + 2 y \leq 120, x + y \geq 60, x - 2 y \geq 0$ and $x \geq 0, y \geq 0,$ then which of the following is/are true ?

Z_{max} = 600

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Z_{min}

is at

(60, 30)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Z_{min} = 300

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Z_{max}

is at

(120, 0)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $Z_{max}$ is at $(120, 0)$
$Z = 5 x + 10 y$ subject to the constraints $x + 2 y \leq 120, x + y \geq 60, x - 2 y \geq 0$ and $x \geq 0, y \geq 0$
We take the given inequality to find the region bounded by these inequalities.
$x + 2 y = 120$
The shaded region $B D E F$ determined by linear inequalities shows the feasible region.
Let us evaluate the objective function $Z$ at each point as shown below

Corner points $Z = 5 x + 10 y$

$B (120, 0)$ $600$

$D (60, 0)$ $300$

$E (40, 20)$ $400$

$F (60, 30)$ $600 (Maximum)$

Hence, Maximum value of $Z$ is $600$ at $F (60, 30)$ and $(120, 0)$ and minimum value of $Z$ is $300$ at $D (60, 0)$

Suggest Corrections

Similar questions

Minimize and maximize Z = 5x + 10y subject to constraints are x + 2y $\leq$ 120, x + y $\geq$ 60, x - 2y $\geq$ 0 and x, y $\geq$ 0.

Q. If

Z = 5 x + 10 y,

subject to the constraints

x + 2 y \leq 120,

x + y \geq 60,

x - 2 y \geq 0

and

x \geq 0, y \geq 0,

then the maximum value of

Z

occurs at

[1 mark]

Minimise and Maximise Z = 5x + 10y

subject to.

Maximize $Z = 5 x + 3 y$ , subject to constraints $3 x + 5 y \leq 15, 5 x + 2 y \leq 10, x \geq 0$ and $y \geq 0$ .

Q. Solve the following problem graphically:
Minimise and Maximise

z = 3 x + 9 y

Subject to the constraints:

x + 3 y \leq 60

x + y \geq 10

x \leq y

x \geq 0, y \geq 0

Join BYJU'S Learning Program

Corner points	$Z = 5 x + 10 y$
$B (120, 0)$	$600$
$D (60, 0)$	$300$
$E (40, 20)$	$400$
$F (60, 30)$	$600 (Maximum)$

If Z=5x+10y, subject to the constraints x+2y≤120,x+y≥60,x−2y≥0 and x≥0,y≥0, then which of the following is/are true ?

If $Z = 5 x + 10 y,$ subject to the constraints $x + 2 y \leq 120, x + y \geq 60, x - 2 y \geq 0$ and $x \geq 0, y \geq 0,$ then which of the following is/are true ?