CBSE Class 12 · 2005 · Linear ProgrammingLong Answer

Solve the following Linear Programming problem graphically:
Maximize $Z=300x+600y$
subject to
$x+2y\le 12$
$2x+y\le 12$
$x+\frac{5}{4}y\ge 5$
$x\ge 0,y\ge 0$

The objective function $Z=ax+by$ of an LPP has maximum value 42 at $(4,6)$ and minimum value 19 at $(3,2)$. Which of the following is true?

The corner points of the feasible region of a linear programming problem are $(0,4)$, $(8,0)$ and $\left(\frac{20}{3},\frac{4}{3}\right)$. If $Z=30x+24y$ is the objective function, then (maximum value of $Z$ $-$ minimum value of $Z$) is equal to:

Solve the following linear programming problem graphically:
Maximize $Z=x+2y$
subject to the constraints
$x+2y\ge 100$
$2x-y\le 0$
$2x+y\le 200$
$x\ge 0,y\ge 0$

The corner points of the feasible region determined by the system of linear inequalities are $(0,0)$, $(4,0)$, $(2,4)$ and $(0,5)$. If the maximum value of $z=ax+by$, where $a,b>0$, occurs at both $(2,4)$ and $(4,0)$, then:

A furniture trader deals in only two items — chairs and tables. He has Rs. 50,000 to invest and a space to store at most 35 items. A chair costs him Rs. 1000 and a table costs him Rs. 2000. The trader earns a profit of Rs. 150 and Rs. 250 on a chair and a table, respectively. For …