Question
Solve the following linear programming problem by graphical method. Under the following constraints :
$
\begin{aligned}
x+2 y & \geq 10 \\
x+y & \geq 6 \\
3 x+y & \geq 8 \\
x, y & \geq 0
\end{aligned}
$
$\operatorname{minimise} Z=3 x+5 y$.

Answer


Image
On drawing all the inequalities on the graph paper, ABCD is the feasible region of this problem where coordinates are as follows :
$A (0,8), B (1,5), C (2,4)$ and $D (10,0)$
Now we shall find the values of $Z$ at these points according to the following table :
Corner PointCorresponding Value of Z = 3x + 5y
A(0, 8)40
B (1, 5)28
C (2, 4)26 Minimum
D(10, 0)30

Hence the minimum value of Z at the corner point C (2, 4) = 26.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

A dealer in rural area wishes to purchase a number of sewing machines. He has only ₹ 5,760 to invest and has space for at most 20 items for storage. An electronic sewing machine costs him  360 and a manually operated sewing machine 240. He can sell the sewing machine at a profit of ₹ 22 and a manually operated sewing machine at a profit of ₹ 18. Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximize his profit? Make it as an LPP and solve it graphically.
Find the points of local maxima or local minima, if any, of the following functions, using the first derivatives test. Also, find the local maximum or local minimum values, as the case may be: 
$\text{f}(\text{x})=\sin2\text{x},0\leq\text{x}\leq\pi$ 
If the marginal cost of maufacturing a certain item is given by $\text{C}(\text{x})=\frac{\text{dC}}{\text{dx}}=2+0.15\text{x}$. Find the total cost function C(x), given that C(0) = 100.
Five bad oranges are accidently mixed with 20 good ones. If four oranges are drawn one by one successively with replacement, then find the probability distribution of number of bad oranges drawn. Hence find the mean and variance of the distribution.
Find a vector of magnitude 6, which is perpendicular to both the vectors $2\hat{\text{i}}-\hat{\text{j}}+2\hat{\text{k}}$ and $4\hat{\text{i}}-\hat{\text{j}}+3\hat{\text{k}}.$
Find the local maximum and local minima, of the function $\text{f(x)} = \sin x - \cos x, 0< x < 2\pi.$ Also find the local maximum and local minimum values.
Determine if f defined by:
$\text{f(x)}=\begin{cases}\text{x}^{2} \sin\frac{1}{\text{x}}, \text{if} \ \text{x}\neq0\\0, \ \ \ \ \ \ \ \ \ \ \ \text{if}\ \text{x} = 0\end{cases}$
Three persons A, B and C apply for a job of Manager in a Private Company. Chances of their selection (A, B and C) are in the ratio $\text{1 : 2 : 4. }$The probabilities that A, B and C can introduce changes to improve profits of the company are 0.8, 0.5 and 0.3 respectively. If the change does not take place, find the probability that it is due to the appointment of C.
Using vector method, prove that the point is collinear:
A(-3, -2, -5), B(1, 2, 3) and C(3, 4, 7)
For what value of $ k$ is the following function continuous at $x = 2$

$f(x) = \begin{matrix} 2x + 1 & ; & x< 2 \\ k & ; & x = 2 \\ 3x - 1 & ; & x> 2 \end{matrix} $