Advertisements
Advertisements
प्रश्न
Which of the following is not a convex set?
पर्याय
{(x, y) : 2x + 5y < 7}
{(x, y) : x2 + y2 ≤ 4}
{x :|x| = 5}
{(x, y) : 3x2 + 2y2 ≤ 6}
उत्तर
{x :|x| = 5}
|x| = 5 is not a convex set as any two points from negative and positive x-axis if are joined will not lie in set.
APPEARS IN
संबंधित प्रश्न
A firm manufactures two types of products A and B and sells them at a profit of Rs 2 on type A and Rs 3 on type B. Each product is processed on two machines M1 and M2. Type A requires one minute of processing time on M1 and two minutes of M2; type B requires one minute on M1 and one minute on M2. The machine M1 is available for not more than 6 hours 40 minutes while machine M2 is available for 10 hours during any working day. Formulate the problem as a LPP.
A rubber company is engaged in producing three types of tyres A, B and C. Each type requires processing in two plants, Plant I and Plant II. The capacities of the two plants, in number of tyres per day, are as follows:
| Plant | A | B | C |
| I | 50 | 100 | 100 |
| II | 60 | 60 | 200 |
The monthly demand for tyre A, B and C is 2500, 3000 and 7000 respectively. If plant I costs Rs 2500 per day, and plant II costs Rs 3500 per day to operate, how many days should each be run per month to minimize cost while meeting the demand? Formulate the problem as LPP.
An automobile manufacturer makes automobiles and trucks in a factory that is divided into two shops. Shop A, which performs the basic assembly operation, must work 5 man-days on each truck but only 2 man-days on each automobile. Shop B, which performs finishing operations, must work 3 man-days for each automobile or truck that it produces. Because of men and machine limitations, shop A has 180 man-days per week available while shop B has 135 man-days per week. If the manufacturer makes a profit of Rs 30000 on each truck and Rs 2000 on each automobile, how many of each should he produce to maximize his profit? Formulate this as a LPP.
A firm manufactures two products, each of which must be processed through two departments, 1 and 2. The hourly requirements per unit for each product in each department, the weekly capacities in each department, selling price per unit, labour cost per unit, and raw material cost per unit are summarized as follows:
| Product A | Product B | Weekly capacity | |
| Department 1 | 3 | 2 | 130 |
| Department 2 | 4 | 6 | 260 |
| Selling price per unit | Rs 25 | Rs 30 | |
| Labour cost per unit | Rs 16 | Rs 20 | |
| Raw material cost per unit | Rs 4 | Rs 4 |
The problem is to determine the number of units to produce each product so as to maximize total contribution to profit. Formulate this as a LPP.
An airline agrees to charter planes for a group. The group needs at least 160 first class seats and at least 300 tourist class seats. The airline must use at least two of its model 314 planes which have 20 first class and 30 tourist class seats. The airline will also use some of its model 535 planes which have 20 first class seats and 60 tourist class seats. Each flight of a model 314 plane costs the company Rs 100,000 and each flight of a model 535 plane costs Rs 150,000. How many of each type of plane should be used to minimize the flight cost? Formulate this as a LPP.
The solution set of the inequation 2x + y > 5 is
Objective function of a LPP is
Which of the following sets are convex?
Let X1 and X2 are optimal solutions of a LPP, then
The maximum value of Z = 4x + 2y subjected to the constraints 2x + 3y ≤ 18, x + y ≥ 10 ; x, y ≥ 0 is
The optimal value of the objective function is attained at the points
The maximum value of Z = 4x + 3y subjected to the constraints 3x + 2y ≥ 160, 5x + 2y ≥ 200, x + 2y ≥ 80; x, y ≥ 0 is
The objective function Z = 4x + 3y can be maximised subjected to the constraints 3x + 4y ≤ 24, 8x + 6y ≤ 48, x ≤ 5, y ≤ 6; x, y ≥ 0
If the constraints in a linear programming problem are changed
The optimum value of the objective function of LPP occurs at the center of the feasible region.
Choose the correct alternative:
How does a constraint, “A washing machine can hold up to 8 kilograms of cloths (X)” can be given?
Tyco Cycles Ltd manufactures bicycles (x) and tricycles (y). The profit earned from the sales of each bicycle and a tricycle are ₹ 400 and ₹ 200 respectively, then the total profit earned by the manufacturer will be given as ______
By spending almost ₹ 250, Rakhi bought some kg grapes (x) and some dozens of bananas (y), then as a constraint this information can be expressed by ______
Heramb requires at most 400 calories from his breakfast. Every morning he likes to take oats and milk. If each bowl of oats and a glass of milk provides him 80 calories and 50 calories respectively, then as a constraint this information can be expressed as ______
Ms. Mohana want to invest at least ₹ 55000 in Mutual funds and fixed deposits. Mathematically this information can be written as ______
Determine the maximum value of Z = 4x + 3y if the feasible region for an LPP is shown in figure
Determine the minimum value of Z = 3x + 2y (if any), if the feasible region for an LPP is shown in Figue.
Solve the following LPP graphically:
Maximise Z = 2x + 3y, subject to x + y ≤ 4, x ≥ 0, y ≥ 0
In maximization problem, optimal solution occurring at corner point yields the ____________.
A type of problems which seek to maximise (or, minimise) profit (or cost) form a general class of problems called.
Conditions under which the object function is to be maximum or minimum are called ______.
