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महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

Choose the correct alternative: How does a constraint, “A washing machine can hold up to 8 kilograms of cloths (X)” can be given? - Mathematics and Statistics

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प्रश्न

Choose the correct alternative:

How does a constraint, “A washing machine can hold up to 8 kilograms of cloths (X)” can be given?

पर्याय

  • X ≥ 8

  • X ≤ 8

  • X ≠ 8

  • X = 8

MCQ
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उत्तर

X ≤ 8

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2.6: Linear Programming - Q.1 (A)

संबंधित प्रश्‍न

Vitamins A and B are found in two different foods F1 and F2. One unit of food F1contains 2 units of vitamin A and 3 units of vitamin B. One unit of food F2 contains 4 units of vitamin A and 2 units of vitamin B. One unit of food F1 and F2 cost Rs 50 and 25 respectively. The minimum daily requirements for a person of vitamin A and B is 40 and 50 units respectively. Assuming that any thing in excess of daily minimum requirement of vitamin A and B is not harmful, find out the optimum mixture of food F1 and F2 at the minimum cost which meets the daily minimum requirement of vitamin A and B. Formulate this as a LPP.


A firm manufactures two products, each of which must be processed through two departments, 1 and 2. The hourly requirements per unit for each product in each department, the weekly capacities in each department, selling price per unit, labour cost per unit, and raw material cost per unit are summarized as follows:
 

  Product A Product B Weekly capacity
Department 1 3 2 130
Department 2 4 6 260
Selling price per unit Rs 25 Rs 30  
Labour cost per unit Rs 16 Rs 20  
Raw material cost per unit Rs 4 Rs 4  


The problem is to determine the number of units to produce each product so as to maximize total contribution to profit. Formulate this as a LPP.


A firm has to transport at least 1200 packages daily using large vans which carry 200 packages each and small vans which can take 80 packages each. The cost of engaging each large van is ₹400 and each small van is ₹200. Not more than ₹3000 is to be spent daily on the job and the number of large vans cannot exceed the number of small vans. Formulate this problem as a LPP given that the objective is to minimize cost


The solution set of the inequation 2x + y > 5 is


Objective function of a LPP is


Which of the following sets are convex?


Let X1 and X2 are optimal solutions of a LPP, then


The optimal value of the objective function is attained at the points


The maximum value of Z = 4x + 3y subjected to the constraints 3x + 2y ≥ 160, 5x + 2y ≥ 200, x + 2y ≥ 80; xy ≥ 0 is


Consider a LPP given by
Minimum Z = 6x + 10y
Subjected to x ≥ 6; y ≥ 2; 2x + y ≥ 10; xy ≥ 0
Redundant constraints in this LPP are 


A company manufactures two types of toys A and B. A toy of type A requires 5 minutes for cutting and 10 minutes for assembling. A toy of type B requires 8 minutes for cutting and 8 minutes for assembling. There are 3 hours available for cutting and 4 hours available for assembling the toys in a day. The profit is ₹ 50 each on a toy of type A and ₹ 60 each on a toy of type B. How many toys of each type should the company manufacture in a day to maximize the profit? Use linear programming to find the solution. 


Tyco Cycles Ltd manufactures bicycles (x) and tricycles (y). The profit earned from the sales of each bicycle and a tricycle are ₹ 400 and ₹ 200 respectively, then the total profit earned by the manufacturer will be given as ______


By spending almost ₹ 250, Rakhi bought some kg grapes (x) and some dozens of bananas (y), then as a constraint this information can be expressed by ______


A doctor prescribed 2 types of vitamin tablets, T1 and T2 for Mr. Dhawan. The tablet T1 contains 400 units of vitamin and T2 contains 250 units of vitamin. If his requirement of vitamin is at least 4000 units, then the inequation for his requirement will be ______


Determine the maximum value of Z = 4x + 3y if the feasible region for an LPP is shown in figure


Determine the minimum value of Z = 3x + 2y (if any), if the feasible region for an LPP is shown in Figue.


Solve the following LPP graphically:
Maximise Z = 2x + 3y, subject to x + y ≤ 4, x ≥ 0, y ≥ 0


A manufacturing company makes two types of television sets; one is black and white and the other is colour. The company has resources to make at most 300 sets a week. It takes Rs 1800 to make a black and white set and Rs 2700 to make a coloured set. The company can spend not more than Rs 648000 a week to make television sets. If it makes a profit of Rs 510 per black and white set and Rs 675 per coloured set, how many sets of each type should be produced so that the company has maximum profit? Formulate this problem as a LPP given that the objective is to maximise the profit.


Minimise Z = 3x + 5y subject to the constraints:
x + 2y ≥ 10
x + y ≥ 6
3x + y ≥ 8
x, y ≥ 0


Feasible region (shaded) for a LPP is shown in the Figure Minimum of Z = 4x + 3y occurs at the point ______.


The common region determined by all the linear constraints of a LPP is called the ______ region.


In maximization problem, optimal solution occurring at corner point yields the ____________.


Conditions under which the object function is to be maximum or minimum are called ______.


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