हिंदी

Refer to Exercise 7 above. Find the maximum value of Z.

Advertisements
Advertisements

प्रश्न

Refer to Exercise 7 above. Find the maximum value of Z.

योग
Advertisements

उत्तर

As per the evaluating table for the value of Z

It is clear that the maximum value of Z is 47 at (3, 2).

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 12: Linear Programming - Exercise [पृष्ठ २५१]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
अध्याय 12 Linear Programming
Exercise | Q 8 | पृष्ठ २५१

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Two tailors, A and B, earn Rs 300 and Rs 400 per day respectively. A can stitch 6 shirts and 4 pairs of trousers while B can stitch 10 shirts and 4 pairs of trousers per day. To find how many days should each of them work and if it is desired to produce at least 60 shirts and 32 pairs of trousers at a minimum labour cost, formulate this as an LPP


Solve the following Linear Programming Problems graphically:

Minimise Z = – 3x + 4 y

subject to x + 2y ≤ 8, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0.


Solve the following Linear Programming Problems graphically:

Minimise Z = x + 2y

subject to 2x + y ≥ 3, x + 2y ≥ 6, x, y ≥ 0.


Show that the minimum of Z occurs at more than two points.

Minimise and Maximise Z = 5x + 10 y

subject to x + 2y ≤ 120, x + y ≥ 60, x – 2y ≥ 0, x, y ≥ 0.


Show that the minimum of Z occurs at more than two points.

Maximise Z = – x + 2y, Subject to the constraints:

x ≥ 3, x + y ≥ 5, x + 2y ≥ 6, y ≥ 0.


A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the time (in minutes) required for each toy on the machines is given below:

Type of toy Machines
I II III
A 12 18 6
B 6 0 9

Each machine is available for a maximum of 6 hours per day. If the profit on each toy of type A is Rs 7.50 and that on each toy of type B is Rs 5, show that 15 toys of type A and 30 of type B should be manufactured in a day to get maximum profit.

 


An aeroplane can carry a maximum of 200 passengers. A profit of Rs 1000 is made on each executive class ticket and a profit of Rs 600 is made on each economy class ticket. The airline reserves at least 20 seats for executive class. However, at least 4 times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of each type must be sold in order to maximize the profit for the airline. What is the maximum profit?


A small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes one hour to make a bracelet and half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is Rs 100 and that on a bracelet is Rs 300. Formulate on L.P.P. for finding how many of each should be produced daily to maximize the profit?

It is being given that at least one of each must be produced.


To maintain his health a person must fulfil certain minimum daily requirements for several kinds of nutrients. Assuming that there are only three kinds of nutrients-calcium, protein and calories and the person's diet consists of only two food items, I and II, whose price and nutrient contents are shown in the table below:
 

  Food I
(per lb)
  Food II
(per lb)
    Minimum daily requirement
for the nutrient
 Calcium 10   5     20
Protein 5   4     20
 Calories 2   6     13
 Price (Rs) 60   100      


What combination of two food items will satisfy the daily requirement and entail the least cost? Formulate this as a LPP.


Maximise Z = 3x + 4y, subject to the constraints: x + y ≤ 1, x ≥ 0, y ≥ 0


Maximise the function Z = 11x + 7y, subject to the constraints: x ≤ 3, y ≤ 2, x ≥ 0, y ≥ 0.


A man rides his motorcycle at the speed of 50 km/hour. He has to spend Rs 2 per km on petrol. If he rides it at a faster speed of 80 km/hour, the petrol cost increases to Rs 3 per km. He has atmost Rs 120 to spend on petrol and one hour’s time. He wishes to find the maximum distance that he can travel. Express this problem as a linear programming problem


Refer to question 15. Determine the maximum distance that the man can travel.


In order to supplement daily diet, a person wishes to take some X and some wishes Y tablets. The contents of iron, calcium and vitamins in X and Y (in milligrams per tablet) are given as below:

Tablets Iron Calcium Vitamin
X 6 3 2
Y 2 3 4

The person needs atleast 18 milligrams of iron, 21 milligrams of calcium and 16 milligrams of vitamin. The price of each tablet of X and Y is Rs 2 and Rs 1 respectively. How many tablets of each should the person take in order to satisfy the above requirement at the minimum cost?


Refer to Question 27. (Maximum value of Z + Minimum value of Z) is equal to ______.


If the feasible region for a LPP is ______ then the optimal value of the objective function Z = ax + by may or may not exist.


A feasible region of a system of linear inequalities is said to be ______ if it can be enclosed within a circle.


A corner point of a feasible region is a point in the region which is the ______ of two boundary lines.


The feasible region for an LPP is always a ______ polygon.


If the feasible region for a LPP is unbounded, maximum or minimum of the objective function Z = ax + by may or may not exist.


Maximum value of the objective function Z = ax + by in a LPP always occurs at only one corner point of the feasible region.


In the given graph, the feasible region for an LPP is shaded. The objective function Z = 2x – 3y will be minimum at:


Objective function of a linear programming problem is ____________.


Z = 7x + y, subject to 5x + y ≥ 5, x + y ≥ 3, x ≥ 0, y ≥ 0. The minimum value of Z occurs at ____________.


In linear programming infeasible solutions


In Corner point method for solving a linear programming problem, one finds the feasible region of the linear programming problem, determines its corner points, and evaluates the objective function Z = ax + by at each corner point. If M and m respectively be the largest and smallest values at corner points then ____________.


In a LPP, the objective function is always ____________.


Maximize Z = 6x + 4y, subject to x ≤ 2, x + y ≤ 3, -2x + y ≤ 1, x ≥ 0, y ≥ 0.


What are constraints in a Linear Programming Problem?


Which statement defines an Optimisation Problem?


Which inequality is one of the given resource constraints in the formulation with objective function \[Z=250x+75y\]?


Which other constraint must be satisfied together with \[5x+y\leq 100\] in the profit-maximization formulation?


What are restrictions on decision variables called in linear programming?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×