Linear Programm...

Minimize: $$z=\sum _{ j=1 }^{ n }{ \sum _{ i=1 }^{ m }{ { c }_{ ij }.{ x }_{ ij } }  } $$
subject to : $$\sum _{ j=1 }^{ n }{ { x }_{ ij }={ a }_{ i } } ,i=1,....m;\quad \sum _{ i=1 }^{ m }{ { x }_{ ij }={ b }_{ j } } ,j=1,....n$$ is a LPP with number of constraints

What is the solution of $$x\le 4,y\ge 0$$ and $$x\le -4,y\le 0$$ ?

The ratio of the rate of flow of water in pipes varies inversely as the square of the radius of the pipes. What is the ratio of the rates of flow in two pipes diameters 2 cm and 4 cm?

The diagram shows a scale drawing of a garden which is p metre long and w metre wide.
(a) Write an inequality between p and w.
(b) If a path of 2 m width is added to two sides as shown in the diagram, write a new inequality between the length and the width.

If $$A=$${1,2,3};$$   B=$$ {3,4,5};$$ C=$${4,6}, then $$A\times (B\cap C)=?$$

The value of $$\displaystyle \frac{0.76\times0.76\times0.76+0.24\times0.24\times0.24 }{0.76\times0.76-0.76\times0.24+0.24\times0.24}$$ is 

The incomplete graph shows Dinesh's savings from January to April.
Dinesh saved a total of RS. 730 during the four months. The amount of money saved in February was as much as that saved in March. How much did he save in March?

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Evaluate $$\displaystyle \frac{(a-b)^{2}}{(b-c)(c-a)}+\frac{(b-c)^{2}}{(a-b)(c-a)}+\frac{(c-a)^{2}}{(a-b)(b-c)}$$