मराठी

Refer to Question 30. Minimum value of F is ______. - Mathematics

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प्रश्न

Refer to Question 30. Minimum value of F is ______.

पर्याय

  • 0

  • – 16

  • 12

  • Does not exist

MCQ
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उत्तर

Refer to Question 30. Minimum value of F is – 16.

Explanation:

The minimum value of F is – 16 at (0, 4).

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पाठ 12: Linear Programming - Exercise [पृष्ठ २५६]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
पाठ 12 Linear Programming
Exercise | Q 31 | पृष्ठ २५६

संबंधित प्रश्‍न

Solve the following Linear Programming Problems graphically:

Maximise Z = 5x + 3y

subject to 3x + 5y ≤ 15, 5x + 2y ≤ 10, 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 = x + 2y 

subject to x + 2y ≥ 100, 2x – y ≤ 0, 2x + y ≤ 200; x, 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.

 


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.


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  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.


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Minimise Z = 13x – 15y subject to the constraints: x + y ≤ 7, 2x – 3y + 6 ≥ 0, x ≥ 0, y ≥ 0


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In figure, the feasible region (shaded) for a LPP is shown. Determine the maximum and minimum value of Z = x + 2y.


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


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In a LPP, the linear inequalities or restrictions on the variables are called ____________.


In a LPP, the objective function is always ______.


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


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.


In a LPP, the minimum value of the objective function Z = ax + by is always 0 if the origin is one of the corner point of the feasible region.


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Maximize Z = 4x + 6y, subject to 3x + 2y ≤ 12, x + y ≥ 4, x, y ≥ 0.


Maximize Z = 7x + 11y, subject to 3x + 5y ≤ 26, 5x + 3y ≤ 30, x ≥ 0, y ≥ 0.


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