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3 questions · 1 auto-graded MCQ + 2 self-marked written.

MCQ 11 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A) :$ It is necessary to find objective function value at every point in the feasible region to find optimum value of the objective function.
Reason $(R) :$ For the constrains $2\text{x}+3\text{y}\leq6,5\text{x}+3\text{y}\leq15,\text{x}\geq0$ and $\text{y}\geq0$ cornner points of the feasible region are $(0, 2), (0, 0)$ and $(3, 0).$
  • A
    $A$ is true, $R$ is true: $R$ is a correct explanation for $A.$
  • B
    $A$ is true $R$ is true; $R$ is not a correct explanation for $A.$
  • C
    $A$ is true: $R$ is false.
  • $A$ is false: $R$ is true.
Answer
Correct option: D.
$A$ is false: $R$ is true.
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Question 21 Mark
Maximise the function $\text{Z}=11\text{x}+7\text{y},$ subject to the constraints: $\text{x}\leq3,\text{y}\leq2,\text{x}\geq0,\text{y}\geq0.$
Answer
Maximise $\text{Z}=11\text{x}+7\text{y},$ subject to the constraints $\text{x}\leq3,\text{y}\leq2,\text{x}\geq0,\text{y}\geq0.$

The shaded region as shown in the figure as OABC is bounded and the coordinates of corner points are (0, 0), (3, 0), (3, 2), and (0, 2), respectively.
Corner points
Corresponding value of Z
(0, 0)
(3, 0)
(3, 2)
(0, 2)
0
33
47 (Maximum)
14
Hence, Z is maximise at (3, 2) and its maximum value is 47.
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Question 31 Mark
Refer to Exercise 7 above. Find the maximum value of Z.
Answer
From question 7, above, it is clear that Z is maximum at (3, 2) and its maximum value is 47.
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