1 Marks Question

Question 11 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 21 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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Question 31 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).

Both A and R are true and R is the correct explanation of A
Both A and R are true but R is NOT the correct explanation of A
A is true but R is false.
A is false but R is true.

Answer

A is false but R is true.

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