Optimization

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...

Let f(.) be a twice differentiable function from R² → R. If p, x₀ ∈ R² where ||p|| is sufficiently small (here ||. || is the Euclidean norm or distance function), then f(x₀ + p) =...

In a supplier-retailer supply chain, the demand of each retailer, the capacity of each supplier, and the unit cost in rupees of material supply from each supplier to each retailer...

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 $...

In a supplier-retailer supply chain, the demand of each retailer, the capacity of each supplier, and the unit cost in rupees of material supply from each supplier to each retailer...

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

The smallest perimeter that a rectangle with area of 4 square units can have is ________ units. (Answer in integer)

The smallest perimeter that a rectangle with area of 4 square units can have is ______ units. (Answer in integer)

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...

Let the superscript T represent the transpose operation. Consider the function $f(x) = \frac{1}{2} x^T Qx - r^T x$, where x and r are $n \times 1$ vectors and Q is a symmetric $n \...

Five jobs (J1, J2, J3, J4 and J5) need to be processed in a factory. Each job can be assigned to any of the five different machines (M1, M2, M3, M4 and M5). The time durations take...

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

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...

Consider the function $$f\left( x \right) = 2{x^3} - 3{x^2}\,\,$$ in the domain $$\,\left[ { - 1,2} \right].$$ The global minimum of $$f(x)$$ is _________.

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...

A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation $$y = 2x\,\,\, - 0.1{x^2}...

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 $$...

The distance between the origin and the point nearest to it on the surface $$\,\,{z^2} = 1 + xy\,\,$$ is

The minimum value of function $$\,\,y = {x^2}\,\,$$ in the interval $$\,\,\left[ {1,5} \right]\,\,$$ is

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}\,...