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प्रश्न
Objective function of LPP is ______.
विकल्प
a constraint
a function to be maximized or minimized
a relation between the decision variables
equation of a straight line
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उत्तर
Objective function of LPP is a function to be maximized or minimized.
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संबंधित प्रश्न
Which of the following statements is correct?
Find the feasible solution of the following inequation:
x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9, 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 company manufactures two types of chemicals Aand B. Each chemical requires two types of raw material P and Q. The table below shows number of units of P and Q required to manufacture one unit of A and one unit of B and the total availability of P and Q.
| Chemical→ | A | B | Availability |
| Raw Material ↓ | |||
| P | 3 | 2 | 120 |
| Q | 2 | 5 | 160 |
The company gets profits of ₹ 350 and ₹ 400 by selling one unit of A and one unit of B respectively. (Assume that the entire production of A and B can be sold). How many units of the chemicals A and B should be manufactured so that the company gets a maximum profit? Formulate the problem as LPP to maximize profit.
A printing company prints two types of magazines A and B. The company earns ₹ 10 and ₹ 15 in magazines A and B per copy. These are processed on three Machines I, II, III. Magazine A requires 2 hours on Machine I, 5 hours on Machine II, and 2 hours on machine III. Magazine B requires 3 hours on machine I, 2 hours on machine II and 6 hours on Machine III. Machines I, II, III are available for 36, 50, and 60 hours per week respectively. Formulate the LPP to determine weekly production of magazines A and B, so that the total profit is maximum.
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 Machine 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. Formulate the LPP to maximize the profit, if he operates the machine M1, for almost 10 hours a day and machine M2 for almost 12 hours a day.
If John drives a car at a speed of 60 km/hour, he has to spend ₹ 5 per km on petrol. If he drives at a faster speed of 90 km/hour, the cost of petrol increases ₹ 8 per km. He has ₹ 600 to spend on petrol and wishes to travel the maximum distance within an hour. Formulate the above problem as L.P.P.
Solve the following LPP by graphical method:
Maximize z = 4x + 6y, subject to 3x + 2y ≤ 12, x + y ≥ 4, x, y ≥ 0.
Minimize z = 6x + 21y, subject to x + 2y ≥ 3, x + 4y ≥ 4, 3x + y ≥ 3, x ≥ 0, y ≥ 0.
Which of the following is correct?
Of all the points of the feasible region, the optimal value of z obtained at the point lies ______.
Solution of LPP to minimize z = 2x + 3y, such that x ≥ 0, y ≥ 0, 1 ≤ x + 2y ≤ 10 is ______.
If the corner points of the feasible solution are (0, 0), (3, 0), (2, 1), `(0, 7/3)` the maximum value of z = 4x + 5y is ______.
The half-plane represented by 3x + 2y < 8 contains the point ______.
Solve each of the following inequations graphically using XY-plane:
4x - 18 ≥ 0
Solve each of the following inequations graphically using XY-plane:
- 11x - 55 ≤ 0
Solve each of the following inequations graphically using XY-plane:
y ≤ - 3.5
Solve the following LPP:
Maximize z = 4x1 + 3x2 subject to
3x1 + x2 ≤ 15, 3x1 + 4x2 ≤ 24, x1 ≥ 0, x2 ≥ 0.
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 firm manufactures two products A and B on which profit earned per unit are ₹ 3 and ₹ 4 respectively. Each product is processed on two machines M1 and M2. The product A requires one minute of processing time on M1 and two minutes of processing time on M2, B requires one minute of processing time on M1 and one minute of processing time on M2. Machine M1 is available for use for 450 minutes while M2 is available for 600 minutes during any working day. Find the number of units of products A and B to be manufactured to get the maximum profit.
A firm manufacturing two types of electrical items A and B, can make a profit of ₹ 20 per unit of A and ₹ 30 per unit of B. Both A and B make use of two essential components a motor and a transformer. Each unit of A requires 3 motors and 2 transformers and each units of B requires 2 motors and 4 transformers. The total supply of components per month is restricted to 210 motors and 300 transformers. How many units of A and B should be manufactured per month to maximize profit? How much is the maximum profit?
In a cattle breeding firm, it is prescribed that the food ration for one animal must contain 14, 22, and 1 unit of nutrients A, B, and C respectively. Two different kinds of fodder are available. Each unit weight of these two contains the following amounts of these three nutrients:
| Nutrient\Fodder | Fodder 1 | Fodder2 |
| Nutrient A | 2 | 1 |
| Nutrient B | 2 | 3 |
| Nutrient C | 1 | 1 |
The cost of fodder 1 is ₹ 3 per unit and that of fodder ₹ 2 per unit. Formulate the L.P.P. to minimize the cost.
Choose the correct alternative :
Of all the points of the feasible region the optimal value of z is obtained at a point
Choose the correct alternative :
Feasible region; the set of points which satify.
Choose the correct alternative :
Solution of LPP to minimize z = 2x + 3y st. x ≥ 0, y ≥ 0, 1≤ x + 2y ≤ 10 is
A train carries at least twice as many first class passengers (y) as second class passengers (x). The constraint is given by ______.
Fill in the blank :
A dish washing machine holds up to 40 pieces of large crockery (x) This constraint is given by_______.
State whether the following is True or False :
The feasible solution of LPP belongs to only quadrant I.
Which value of x is in the solution set of inequality − 2X + Y ≥ 17
Maximize z = 5x + 2y subject to 3x + 5y ≤ 15, 5x + 2y ≤ 10, x ≥ 0, y ≥ 0
Maximize z = 7x + 11y subject to 3x + 5y ≤ 26, 5x + 3y ≤ 30, x ≥ 0, y ≥ 0
Maximize z = 10x + 25y subject to x + y ≤ 5, 0 ≤ x ≤ 3, 0 ≤ y ≤ 3
Minimize z = 7x + y subjected to 5x + y ≥ 5, x + y ≥ 3, x ≥ 0, y ≥ 0.
Minimize z = 2x + 4y is subjected to 2x + y ≥ 3, x + 2y ≥ 6, 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
State whether the following statement is True or False:
LPP is related to efficient use of limited resources
A company produces two types of pens A and B. Pen A is of superior quality and pen B is of lower quality. Profits on pens A and B are ₹ 5 and ₹ 3 per pen respectively. Raw materials required for each pen A is twice as that of pen B. The supply of raw material is sufficient only for 1000 pens per day. Pen A requires a special clip and only 400 such clips are available per day. For pen B, only 700 clips are available per day. Formulate this problem as a linear programming problem.
Solve the following linear programming problems by graphical method.
Maximize Z = 20x1 + 30x2 subject to constraints 3x1 + 3x2 ≤ 36; 5x1 + 2x2 ≤ 50; 2x1 + 6x2 ≤ 60 and x1, x2 ≥ 0.
In the given graph the coordinates of M1 are
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
A firm manufactures two products A and B on which the profits earned per unit are ₹ 3 and ₹ 4 respectively. Each product is processed on two machines M1 and M2. Product A requires one minute of processing time on M1 and two minutes on M2, While B requires one minute on M1 and one minute on M2. Machine M1 is available for not more than 7 hrs 30 minutes while M2 is available for 10 hrs during any working day. Formulate this problem as a linear programming problem to maximize the profit.
The LPP to maximize Z = x + y, subject to x + y ≤ 1, 2x + 2y ≥ 6, x ≥ 0, y ≥ 0 has ________.
The minimum value of z = 5x + 13y subject to constraints 2x + 3y ≤ 18, x + y ≥ 10, x ≥ 0, y ≥ 2 is ______
Solve the following LP.P.
Maximize z = 13x + 9y,
Subject to 3x + 2y ≤ 12,
x + y ≥ 4,
x ≥ 0,
y ≥ 0.
Food F1 contains 2, 6, 1 units and food F2 contains 1, 1, 3 units of proteins, carbohydrates, fats respectively per kg. 8, 12 and 9 units of proteins, carbohydrates and fats is the weekly minimum requirement for a person. The cost of food F1 is Rs. 85 and food F2 is Rs. 40 per kg. Formulate the L.P.P. to minimize the cost.
