हिंदी

Choose the correct alternative: The corner points of the feasible region are (0, 3), (3, 0), (8, 0), (125,385) and (0, 10), then the point of maximum Z = 6x + 4y = 48 is at - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Choose the correct alternative:

The corner points of the feasible region are (0, 3), (3, 0), (8, 0), `(12/5, 38/5)` and (0, 10), then the point of maximum Z = 6x + 4y = 48 is at

विकल्प

  • (0, 10)

  • (8, 0)

  • `(12/5, 38/5)`

  • (3, 0)

MCQ
Advertisements

उत्तर

(8, 0)

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2.6: Linear Programming - Q.1 (A)

संबंधित प्रश्न

A company produces two types of goods A and B, that require gold and silver. Each unit of type A requires 3 g of silver and 1 g of golds while that of type B requires 1 g of silver and 2 g of gold. The company can procure a maximum of 9 g of silver and 8 g of gold. If each unit of type A brings a profit of Rs 40 and that of type B Rs 50, formulate LPP to maximize profit.


A small manufacturing firm produces two types of gadgets A and B, which are first processed in the foundry, then sent to the machine shop for finishing. The number of man-hours of labour required in each shop for the production of each unit of and B, and the number of man-hours the firm has available per week are as follows:

Gadget Foundry Machine-shop
A 10 5
B 6 4
 Firm's capacity per week 1000 600

The profit on the sale of A is Rs 30 per unit as compared with Rs 20 per unit of B. The problem is to determine the weekly production of gadgets A and B, so that the total profit is maximized. Formulate this problem as a LPP.

 


 


A firm manufactures 3 products AB and C. The profits are Rs 3, Rs 2 and Rs 4 respectively. The firm has 2 machines and below is the required processing time in minutes for each machine on each product : 

Machine Products
A B C
M1
M2
4 3 5
2 2 4

Machines M1 and M2 have 2000 and 2500 machine minutes respectively. The firm must manufacture 100 A's, 200 B's and 50 C's but not more than 150 A's. Set up a LPP to maximize the profit.


Amit's mathematics teacher has given him three very long lists of problems with the instruction to submit not more than 100 of them (correctly solved) for credit. The problem in the first set are worth 5 points each, those in the second set are worth 4 points each, and those in the third set are worth 6 points each. Amit knows from experience that he requires on the average 3 minutes to solve a 5 point problem, 2 minutes to solve a 4 point problem, and 4 minutes to solve a 6 point problem. Because he has other subjects to worry about, he can not afford to devote more than

\[3\frac{1}{2}\] hours altogether to his mathematics assignment. Moreover, the first two sets of problems involve numerical calculations and he knows that he cannot stand more than 
\[2\frac{1}{2}\]  hours work on this type of problem. Under these circumstances, how many problems in each of these categories shall he do in order to get maximum possible credit for his efforts? Formulate this as a LPP.

 


A farmer has a 100 acre farm. He can sell the tomatoes, lettuce, or radishes he can raise. The price he can obtain is Rs 1 per kilogram for tomatoes, Rs 0.75 a head for lettuce and Rs 2 per kilogram for radishes. The average yield per acre is 2000 kgs for radishes, 3000 heads of lettuce and 1000 kilograms of radishes. Fertilizer is available at Rs 0.50 per kg and the amount required per acre is 100 kgs each for tomatoes and lettuce and 50 kilograms for radishes. Labour required for sowing, cultivating and harvesting per acre is 5 man-days for tomatoes and radishes and 6 man-days for lettuce. A total of 400 man-days of labour are available at Rs 20 per man-day. Formulate this problem as a LPP to maximize the farmer's total profit.


Solve the following L.P.P. by graphical method :

Minimize : Z = 7x + y subject to 5x + y ≥ 5, x + y ≥ 3, x ≥ 0, y ≥ 0.


Choose the correct alternative :

The point at which the maximum value of z = x + y subject to the constraints x + 2y ≤ 70, 2x + y ≤ 95, x ≥ 0, y ≥ 0 is


Fill in the blank :

Graphical solution set of the in equations x ≥ 0, y ≥ 0 is in _______ quadrant


Fill in the blank :

The region represented by the in equations x ≤ 0, y ≤ 0 lines in _______ quadrants.


The constraint that a factory has to employ more women (y) than men (x) is given by _______


Solve the following problem:

Maximize Z = 4x1 + 3x2 Subject to 3x1 + x2 ≤ 15, 3x1 + 4x2 ≤ 24, x1 ≥ 0, x2 ≥ 0


Choose the correct alternative:

If LPP has optimal solution at two point, then


Choose the correct alternative:

The point at which the minimum value of Z = 8x + 12y subject to the constraints 2x + y ≥ 8, x + 2y ≥ 10, x ≥ 0, y ≥ 0 is obtained at the point


Choose the correct alternative:

The corner points of the feasible region are (4, 2), (5, 0), (4, 1) and (6, 0), then the point of minimum Z = 3.5x + 2y = 16 is at


State whether the following statement is True or False:

If LPP has two optimal solutions, then the LPP has infinitely many solutions


State whether the following statement is True or False:

A convex set includes the points but not the segment joining the points


State whether the following statement is True or False:

Of all the points of feasible region, the optimal value is obtained at the boundary of the feasible region


State whether the following statement is True or False:

The graphical solution set of the inequations 0 ≤ y, x ≥ 0 lies in second quadrant


The feasible region represented by the inequations x ≥ 0, y ≤ 0 lies in ______ quadrant.


A dealer deals in two products X and Y. He has ₹ 1,00,000/- to invest and space to store 80 pieces. Product X costs ₹ 2500/- and product Y costs ₹ 1000/- per unit. He can sell the items X and Y at respective profits of ₹ 300 and ₹ 90. Construct the LPP and find the number of units of each product to be purchased to maximize its profit


A company manufactures two types of ladies dresses C and D. The raw material and labour available per day is given in the table.

Resources Dress C(x) Dress D(y) Max. availability
Raw material 5 4 60
Labour 5 3 50

P is the profit, if P = 50x + 100y, solve this LPP to find x and y to get the maximum profit


Maximize Z = 5x + 10y subject to constraints

x + 2y ≤ 10, 3x + y ≤ 12, x ≥ 0, y ≥ 0


Minimize Z = 24x + 40y subject to constraints

6x + 8y ≥ 96, 7x + 12y ≥ 168, x ≥ 0, y ≥ 0


Minimize Z = x + 4y subject to constraints

x + 3y ≥ 3, 2x + y ≥ 2, x ≥ 0, y ≥ 0


Solve the following LPP graphically:

Maximize Z = 9x + 13y subject to constraints

2x + 3y ≤ 18, 2x + y ≤ 10, x ≥ 0, y ≥ 0

Solution: Convert the constraints into equations and find the intercept made by each one of it.

Inequation Equation X intercept Y intercept Region
2x + 3y ≤ 18 2x + 3y = 18 (9, 0) (0, ___) Towards origin
2x + y ≤ 10 2x + y = 10 ( ___, 0) (0, 10) Towards origin
x ≥ 0, y ≥ 0 x = 0, y = 0 X axis Y axis ______

The feasible region is OAPC, where O(0, 0), A(0, 6),

P( ___, ___ ), C(5, 0)

The optimal solution is in the following table:

Point Coordinates Z = 9x + 13y Values Remark
O (0, 0) 9(0) + 13(0) 0  
A (0, 6) 9(0) + 13(6) ______  
P ( ___,___ ) 9( ___ ) + 13( ___ ) ______ ______
C (5, 0) 9(5) + 13(0) ______  

∴ Z is maximum at __( ___, ___ ) with the value ___.


If z = 200x + 500y  .....(i)

Subject to the constraints:

x + 2y ≥ 10  .......(ii)

3x + 4y ≤ 24  ......(iii)

x, 0, y ≥ 0  ......(iv)

At which point minimum value of Z is attained.


Shraddho wants to invest at most ₹ 25,000/- in saving certificates and fixed deposits. She wants to invest at least ₹ 10,000/- in saving certificate and at least ₹ 15,000/- in fixed deposits. The rate of interest on saving certificate is 5% and that on fixed deposits is 7% per annum. Formulate the above problem as LPP to determine maximum income yearly.


Graphical solution set of the inequations x ≥ 0 and y ≤ 0 lies in ______ quadrant.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×