Linear Programming

An objective function Z of primal variables (x₁ and x₂) is described below: Minimize Z = 0.07 x₁ + 0.05 x₂ subject to 0.1 x₁ ≥ 0.4 0.1 x₂ ≥ 0.6 0.1 x₁ + 0.2 x₂ ≥ 2.0 0.2 x₁ + 0.1 x...

At the current basic feasible solution (bfs) $\boldsymbol{v_0}$ ($\boldsymbol{v_0} \in \mathbb{R}^5$), the simplex method yields the following form of a linear programming problem...

At the current basic feasible solution (bfs) $v_0 (v_0 \in \mathbb{R}^5)$, the simplex method yields the following form of a linear programming problem in standard form: minimize $...

Which one of the options given represents the feasible region of the linear programming model: Maximize 45X1 + 60X2 X1 ≤ 45 X2 ≤ 50 10X1 + 10X2 ≥ 600 25X1 + 5X2 ≤ 750

In a linear programming problem, if a resource is not fully utilized, the shadow price of that resource is

A manufacturing unit produces two products Pl and P2. For each piece of P1 and P2, the table below provides quantities of materials M1, M2, and M3 required, and also the profit ear...

A factory produces m (i = 1,2,..., m) products, each of which requires processing on n (j = 1, 2, ..., n) workstations. Let aij be the amount of processing time that one unit of th...

The problem of maximizing z = x₁-x₂ subject to constraints x₁ + x₂ ≤10, x₁ ≥ 0, x₂ ≥ 0 and x₂ ≤5 has

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 5 hours and 3 hours, respectively, while the total pr...

The minimum value of 3x + 5y such that: 3x + 5y ≤ 15 4x + 9y ≤ 8 13x + 2y ≤ 2 x ≥ 0, y ≥ 0 is ________.

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 $$5$$ hours and $$3$$ hours,...

Maximize $$\,\,\,\,Z = 15{x_1} + 20{x_2}$$ Subject to $$\eqalign{ & 12{x_1} + 4{x_2} \ge 36 \cr & 12{x_1} - 6{x_2} \le 24 \cr & \,\,\,\,\,\,\,\,\,{x_1},\,\,{x_2} \ge 0 \cr} $$ The...

For the linear programming problem: $$\eqalign{ & Maximize\,\,\,\,\,Z = 3{x_1} + 2{x_2} \cr & Subject\,\,to\,\,\,\, - 2{x_1} + 3{x_2} \le 9 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...

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 & {x_1} + 2{x_2} \le 4, \cr & {x_1} \g...

A linear programming problem is shown below. $$\eqalign{ & Maximize\,\,\,\,3x + 7y \cr & Subject\,\,to\,\,\,3x + 7y \le 10 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4x...

One unit of product $${P_1}$$ requires $$3$$ $$kg$$ of resource $${R_1}$$ and $$1$$ $$kg$$ of resource $${R_2}$$. One unit of product $${P_2}$$ requires $$2$$ $$kg$$ of resource $$...

One unit of product $${P_1}$$ requires $$3$$ $$kg$$ of resource $${R_1}$$ and $$1$$ $$kg$$ of resource $${R_2}$$. One unit of product $${P_2}$$ requires $$2$$ $$kg$$ of resource $$...

Simplex method of solving linear programming problem uses

Consider the following Linear Programming problem $$(LLP)$$ Maximize: $$Z = 3{x_1} + 2{x_2}$$ $$\,\,$$ Subject $$\,\,$$ to $$\eqalign{ & \,\,\,\,\,\,\,{x_1} \le 4 \cr & \,\,\,\,\,\...

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

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

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 units per day. The supply of r...

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$$2{x_1} + 5{x_2}.$$ The product...

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

Solve the following linear programming problem by simplex method $$\eqalign{ & Maximize\,\,\,\,\,\,4{x_1} + 6{x_2} + {x_3} \cr & Subject\,\,to\,\,\,\,\,\,2{x_1} - {x_2} + 3{x_3}\,...

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