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Linear programming Maths - Linear programming

Maharashtra Board - STD 12 - Maths (MSBSHSE - Semi English Medium). 133 questions in this chapter.

Question types

Linear programming question types

133 questions across 2 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

133
Questions
2
Question groups
5
Question types
Sample Questions

Linear programming questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1MCQ1 Mark
The maximum value of $Z = 4x + 2y$ Subjected to the constraints $2\text{x}+3\text{y}\leq18,\text{x}+\text{y}\geq10,\text{x},\text{y}\geq0$ is:
  • A
    $36$
  • B
    $40$
  • C
    $20$
  • ✓
    none of these

Answer: D.

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Q 2MCQ1 Mark
Objective function of a $\text{LPP}$ is:
  • A
    a constraint
  • ✓
    a function to be optimized
  • C
    a relation between the variables
  • D
    none of these

Answer: B.

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Q 3MCQ1 Mark
The maximum value of $Z = 4x + 3y$ subjected to the constraints $3x + 2y ≥ 160, 5x + 2y ≥ 200, x + 2y ≥ 80, x, y ≥ 0$ is:
  • A
    $320$
  • B
    $300$
  • C
    $230$
  • ✓
    none of these

Answer: D.

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Q 4MCQ1 Mark
The corner points of the feasible region determined by the following system of linear inequalities:
$2x + y \leq 10, x + 3y \leq 15, x, y \geq 0$ are $(0, 0), (5, 0), (3, 4)$ and $(0, 5).$
Let $Z = px + qy,$ where $p.q > 0.$
Condition on $p$ and $q$ so that the maximum of $Z$ occurs at both $(3, 4)$ and $(0, 5)$ is:
  • A
    $P = q$
  • B
    $p = 2q$
  • C
    $p = 3q$
  • ✓
    $q = 3q$

Answer: D.

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Q 5MCQ1 Mark
The objective function $Z = 4x + 3y$ can be maximised subjected to the constraints $3x + 4y ≤ 24, 8x + 6y ≤ 48, x ≤ 5, y ≤ 6, x, y ≥ 0$
  • A
    at only one point
  • B
    at two points only
  • ✓
    at an infinite number of points
  • D
    none of these

Answer: C.

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Q 6Solve the Following Question.(5 Marks)5 Marks
A wholesale dealer deals in two kinds, $A$ and $B$ (say) of mixture of nuts. Each kg of mixture $A$ contains 60 grams of almonds, 30 grams of cashew nuts and 30 grams of hazel nuts. Each kg of mixture B contains 30 grams of almonds, 60 grams of cashew nuts and 180 grams of hazel nuts. The remainder of both mixtures is per nuts. The dealer is contemplating to use mixtures A and B to make a bag which will contain at least 240 grams of almonds, 300 grams of cashew nuts and 540 grams of hazel nuts. Mixture $A$ costs Rs. 8 per kg. and mixture $B$ costs Rs. 12 per kg. Assuming that mixtures $A$ and $B$ are uniform, use graphical method to determine the number of kg . of each mixture which he should use to minimise the cost of the bag.
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Q 7Solve the Following Question.(5 Marks)5 Marks
A farmer mixes two brands P and Q of cattle feed. Brand P, costing Rs. 250 per bag, contains 3 units of nutritional element A, 2.5 units of element B and 2 units of element C. Brand Q costing Rs. 200 per bag contains 1.5 units of nutritional element A, 11.25 units of element B and 3 units of element C. The minimum requirements of nutrients A, B and C are 18 units, 45 units and 24 units respectively. Determine the number of bags of each brand which should be mixed in order to produce a mixture having a minimum cost per bag? What is the minimum cost of the mixture per bag?
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Q 8Solve the Following Question.(5 Marks)5 Marks
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 atleast 20 seats for executive class. However, atleast 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 maximise the profit of the airline. What is the maximum profit?
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Q 9Solve the Following Question.(5 Marks)5 Marks
A dietician mixes together two kinds of food in such a way that the mixture contains at least 6 units of vitamin A, 7 units of vitamin B, 11 units of vitamin C and 9 units of vitamin D. The vitamin contents of 1kg of food X and 1kg of food Y are given below:
 
Vitamin
A
Vitamin
B
Vitamin
C
Vitamin
D
Food X
1
1
1
2
Food Y
2
1
3
1
One kg food X costs Rs. 5, whereas one kg of food Y costs Rs. 8.
Find the least cost of the mixture which will produce the desired diet.
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