Algebra

Linear Programming

Easy

Case Study

A dietician wishes to mix two types of foods in such a way that vitamin contents of the mixture contain at least 8 units of vitamin A and 10 units of vitamin C. Food 'I' contains 2 unit/kg of vitamin A and 1 unit/kg of vitamin C. Food 'II' contains 1 unit/kg of vitamin A and 2 unit/kg of vitamin C. It cost Rs.50 per kg to purchase Food 'I' and Rs 70 per kg to purchase Food 'II'

Let x kg of food 'I' and y kg of food 'II' be mixed together for daily vitamin requirement in the family at minimum cost. Based on this information answer the question:

The feasible solution to the LPP is-

$x = 2, y = 4$

$x = 4, y = 2$

Does not exist

$x = 4, y = 0$

✅ Correct Option: 1

Evaluating $z = 50x + 70y$ at corner points: $(0,8): 560$ , $(2,4): 380$ , $(10,0): 500$ . Minimum cost is at $(2, 4)$ , so $x = 2, y = 4$ .

Question 41

Objective function of LPP is:

Question 42

The constraints are -

A. $2x + y \leq 8$

B. $2x + y \geq 8$

C. $x + 2y \leq 10$

D. $x + 2y \geq 10$

E. $x, y \geq 0$

Choose the correct answer from the options given below:

Question 43

The type of feasible region and its corner points are.

A. bounded

B. unbounded

C. (0,5), (2,4), (10,0)

D. (0,8), (2,4), (4,0)

E. (0,8), (2,4), (10,0)

Choose the correct answer from the options given below:

Question 45

The minimum cost of the mixture is-

The feasible solution to the LPP is-

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)