3 Marks Question

Question 13 Marks

Solve the following LPP graphically:
Maximize Z = 1000x + 600y
subject to the constraints
$\begin{aligned} x+y & \leq 200 \\ x & \geq 20 \\ y-4 x & \geq 0 \\ x, y & \geq 0\end{aligned}$

Answer

Corner points	Value of Z = 1000x + 600y
(20,80) (40, 160) (20, 180)	68,000 $1,36,000 \rightarrow$ Maximum 1,28,000

$\therefore$ Maximum value, Z = 1, 36000
at x = 40 y = 160

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Question 23 Marks

Solve the following linear programming problem graphically:
Minimize: Z = 3x + 9y
When: $x+3 y \leq 60$
$\begin{aligned} x+y & \geq 10 \\ x & \leq y \\ x & \geq 0, y \geq 0\end{aligned}$

Answer

Vertices of feasible region are
A(0, 20) B(15, 15) C(5,5) D(0, 10)

Corner points	Value of Z = 1000x + 600y
(0,20) (15, 15) (5,5) (0, 10)	180 180 $60 \rightarrow$ minimum 90

$\therefore$Z = 60 is minimum at x = 5, y = 5

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Question 33 Marks

Solve the following linear programming problem graphically:
Minimize: Z = 6x + 3y
Subject to the constraints: $\left\{\begin{array}{c}4 x+y \geq 80 \\ x+5 y \geq 115 \\ 3 x+2 y \leq 150 \\ x \geq 0, y \geq 0\end{array}\right.$

Answer

Corner points	Value of z
A(40, 15)	285
(B (15,20))	150 → Minimum
(C (2,72))	228
Minimum	Z=150
when	x=15,y=20

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Question 43 Marks

Solve the following LPP graphically:
Maximize z = 4x + y
Subject to following constraints
$\begin{aligned} x+y & \leq 50 \\ 3 x+y & \leq 90 \\ x & \geq 10 \\ x, y & \geq 0\end{aligned}$

Answer

$\begin{aligned}\left.Z\right|_{A(10,0)} & =40 \\ \left.Z\right|_{B(30,0)} & =120 \rightarrow \text { Maximum }\end{aligned}$
$\begin{array}{l}\left.Z\right|_{C(20,30)}=110 \\ \left.Z\right|_{D(10,40)}=80\end{array}$
Maximum value, Z = 120 at (30, 0)

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Question 53 Marks

Solve the following LPP graphically:
Minimize Z = 5x + 10y
Subject to $x+2 y \leq 120$
Constraints $\begin{aligned} x+y & \geq 60 \\ x-2 y & \geq 0\end{aligned}$
and $x, y \geq 0$

Answer

Z = 5x + 10y
$\begin{aligned}\left. Z \right|_{A(60,0)} & =300 \rightarrow \text { Minimum } \\ \left. Z \right|_{B(120,0)} & =600 \\ \left. Z \right|_{C(60,30)} & =600 \\ \left. Z \right|_{D(40,20)} & =400\end{aligned}$
Minimum value, Z = 300 at x = 60 y = 0

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Applied Maths 3 Marks Question

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