## Marks 1

Simplex method of solving linear programming problem uses

If at the optimum in a linear programming problem, a dual variable corresponding to a particular primal constraint is zero, then it means that

## Marks 2

Maximize $$\,\,\,\,\,\,\,\,\,Z = 5{x_1} + 3{x_2}$$
Subject to $$\,\,\,\,\,\,\,\,\,\,{x_1} + 2{x_2} \le 10,$$
$$\eqalign{
& \,\,\,\,\,\,\,\,\,\,...

Two models, $$P$$ and $$Q,$$ of a product earn profits of Rs. $$100$$ and Rs. $$80$$ per piece, respectively. Production times for $$P$$ and $$Q$$ are...

A firm uses a turning center, a milling center and a grinding machine to produce two parts. The table below provides the
machining time required for...

Maximize $$\,\,\,\,Z = 15{x_1} + 20{x_2}$$
Subject to
$$\eqalign{
& 12{x_1} + 4{x_2} \ge 36 \cr
& 12{x_1} - 6{x_2} \le 24 \cr
&...

For the linear programming problem:
$$\eqalign{
& Maximize\,\,\,\,\,Z = 3{x_1} + 2{x_2} \cr
& Subject\,\,to\,\,\,\, - 2{x_1} + 3{x_2} \...

Consider an objective function $$Z\left( {{x_1},{x_2}} \right) = 3{x_1} + 9{x_2}$$ and the constraints
$$\eqalign{
& {x_1} + {x_2} \le 8, \cr ...

A linear programming problem is shown below.
$$\eqalign{
& Maximize\,\,\,\,3x + 7y \cr
& Subject\,\,to\,\,\,3x + 7y \le 10 \cr
&...

One unit of product $${P_1}$$ requires $$3$$ $$kg$$ of resource $${R_1}$$ and $$1$$ $$kg$$ of resource $${R_2}$$. One unit of product $${P_2}$$ requir...

One unit of product $${P_1}$$ requires $$3$$ $$kg$$ of resource $${R_1}$$ and $$1$$ $$kg$$ of resource $${R_2}$$. One unit of product $${P_2}$$ requir...

Consider the following Linear Programming problem $$(LLP)$$
Maximize: $$Z = 3{x_1} + 2{x_2}$$
$$\,\,$$ Subject $$\,\,$$ to
$$\eqalign{
& \,\,\,...

Consider the Linear programme $$(LP)$$
Max $$4x$$ + $$6y$$
Subject to
$$\eqalign{
& \,\,\,\,\,\,\,\,\,\,\,3x + 2y \le 6 \cr
& \,\,\,\,...

Consider the Linear programme $$(LP)$$
Max $$4x$$ + $$6y$$
Subject to
$$\eqalign{
& \,\,\,\,\,\,\,\,\,\,\,3x + 2y \le 6 \cr
& \,\,\,\,...

Consider a linear programming problem with two variables and two constraints. The objective function is: Maximize $${x_1} + {x_2}.$$ The corner points...

Consider a linear programming problem with two variables and two constraints. The objective function is: Maximize $${x_1} + {x_2}.$$ The corner points...

A company produces two types of toys: $$P$$ and $$Q.$$ Production time of $$Q$$ is twice that of $$P$$ and the company has a maximum of $$2000$$ time ...

A manufacturer produces two types of products, $$1$$ and $$2,$$ at production levels of $${x_1}$$ and $${x_2}$$ respectively. The profit is given is$...

## Marks 5

A furniture manufacturer produces chairs and tables. The wood-working department is capable of producing $$200$$ chairs or $$100$$ tables or any propo...

Solve the following linear programming problem by simplex method
$$\eqalign{
& Maximize\,\,\,\,\,\,4{x_1} + 6{x_2} + {x_3} \cr
& Subjec...