Advertisements
Advertisements
प्रश्न
State whether the following is True or False :
The feasible solution of LPP belongs to only quadrant I.
विकल्प
True
False
Advertisements
उत्तर
The feasible solution of LPP belongs to only quadrant I True.
APPEARS IN
संबंधित प्रश्न
Find the feasible solution of the following inequation:
2x + 3y ≤ 6, x + y ≥ 2, x ≥ 0, y ≥ 0
Find the feasible solution of the following inequations:
x - 2y ≤ 2, x + y ≥ 3, - 2x + y ≤ 4, x ≥ 0, y ≥ 0
A furniture dealer deals in tables and chairs. He has ₹ 1,50,000 to invest and a space to store at most 60 pieces. A table costs him ₹ 1500 and a chair ₹ 750. Construct the inequations and find the feasible solution.
A manufacturing firm produces two types of gadgets A and B, which are first processed in the foundry and then sent to the machine shop for finishing. The number of man-hours of labour required in each shop for production of A and B per unit and the number of man-hours available for the firm is as follows:
| Gadgets | Foundry | Machine shop |
| A | 10 | 5 |
| B | 6 | 4 |
| Time available (hour) | 60 | 35 |
Profit on the sale of A is ₹ 30 and B is ₹ 20 per units. Formulate the L.P.P. to have maximum profit.
A doctor has prescribed two different units of foods A and B to form a weekly diet for a sick person. The minimum requirements of fats, carbohydrates and proteins are 18, 28, 14 units respectively. One unit of food A has 4 units of fat, 14 units of carbohydrates and 8 units of protein. One unit of food B has 6 units of fat, 12 units of carbohydrates and 8 units of protein. The price of food A is ₹ 4.5 per unit and that of food B is ₹ 3.5 per unit. Form the LPP, so that the sick person’s diet meets the requirements at a minimum cost.
Solve the following LPP by graphical method:
Maximize z = 7x + 11y, subject to 3x + 5y ≤ 26, 5x + 3y ≤ 30, x ≥ 0, y ≥ 0.
Solve the following L.P.P. by graphical method:
Minimize: z = 8x + 10y
Subject to: 2x + y ≥ 7, 2x + 3y ≥ 15, y ≥ 2, x ≥ 0, y ≥ 0.
Minimize z = 6x + 21y, subject to x + 2y ≥ 3, x + 4y ≥ 4, 3x + y ≥ 3, x ≥ 0, y ≥ 0.
Solve the following LPP:
Maximize z = 2x + 3y subject to x - y ≥ 3, x ≥ 0, y ≥ 0.
Solve each of the following inequations graphically using XY-plane:
y ≤ - 3.5
A carpenter makes chairs and tables. Profits are ₹ 140 per chair and ₹ 210 per table. Both products are processed on three machines: Assembling, Finishing and Polishing. The time required for each product in hours and availability of each machine is given by the following table:
| Product → | Chair (x) | Table (y) | Available time (hours) |
| Machine ↓ | |||
| Assembling | 3 | 3 | 36 |
| Finishing | 5 | 2 | 50 |
| Polishing | 2 | 6 | 60 |
Formulate the above problem as LPP. Solve it graphically
A manufacturer produces bulbs and tubes. Each of these must be processed through two machines M1 and M2. A package of bulbs requires 1 hour of work on Machine M1 and 3 hours of work on M2. A package of tubes requires 2 hours on Machine M1 and 4 hours on Machine M2. He earns a profit of ₹ 13.5 per package of bulbs and ₹ 55 per package of tubes. If maximum availability of Machine M1 is 10 hours and that of Machine M2 is 12 hours, then formulate the L.P.P. to maximize the profit.
Choose the correct alternative :
Which of the following is correct?
Choose the correct alternative :
The corner points of the feasible region are (0, 0), (2, 0), `(12/7, 3/7)` and (0,1) then the point of maximum z = 7x + y
Choose the correct alternative :
The half plane represented by 3x + 2y ≤ 0 constraints the point.
Choose the correct alternative :
The half plane represented by 4x + 3y ≥ 14 contains the point
State whether the following is True or False :
The point (1, 2) is not a vertex of the feasible region bounded by 2x + 3y ≤ 6, 5x + 3y ≤ 15, x ≥ 0, y ≥ 0.
The point of which the maximum value of z = x + y subject to constraints x + 2y ≤ 70, 2x + y ≤ 90, x ≥ 0, y ≥ 0 is obtained at
Minimize z = 6x + 21y subject to x + 2y ≥ 3, x + 4y ≥ 4, 3x + y ≥ 3, x ≥ 0, y ≥ 0 show that the minimum value of z occurs at more than two points
Choose the correct alternative:
The feasible region is
Choose the correct alternative:
Z = 9x + 13y subjected to constraints 2x + 3y ≤ 18, 2x + y ≤ 10, 0 ≤ x, y was found to be maximum at the point
State whether the following statement is True or False:
Objective function of LPP is a relation between the decision variables
A company produces two types of products say type A and B. Profits on the two types of product are ₹ 30/- and ₹ 40/- per kg respectively. The data on resources required and availability of resources are given below.
| Requirements | Capacity available per month | ||
| Product A | Product B | ||
| Raw material (kgs) | 60 | 120 | 12000 |
| Machining hours/piece | 8 | 5 | 600 |
| Assembling (man hours) | 3 | 4 | 500 |
Formulate this problem as a linear programming problem to maximize the profit.
Solve the following linear programming problems by graphical method.
Maximize Z = 6x1 + 8x2 subject to constraints 30x1 + 20x2 ≤ 300; 5x1 + 10x2 ≤ 110; and x1, x2 ≥ 0.
Solve the following linear programming problems by graphical method.
Minimize Z = 3x1 + 2x2 subject to the constraints 5x1 + x2 ≥ 10; x1 + x2 ≥ 6; x1 + 4x2 ≥ 12 and x1, x2 ≥ 0.
Given an L.P.P maximize Z = 2x1 + 3x2 subject to the constrains x1 + x2 ≤ 1, 5x1 + 5x2 ≥ 0 and x1 ≥ 0, x2 ≥ 0 using graphical method, we observe
Sketch the graph of the following inequation in XOY co-ordinate system.
2y - 5x ≥ 0
