Introduction of Linear Programming

Ms. Mohana want to invest at least ₹ 55000 in Mutual funds and fixed deposits. Mathematically this information can be written as ______

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

State whether the following statement is True or False:

The half-plane represented by 3x + 4y ≥ 12 includes the point (4, 3)

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

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.

Heramb requires at most 400 calories from his breakfast. Every morning he likes to take oats and milk. If each bowl of oats and a glass of milk provides him 80 calories and 50 calories respectively, then as a constraint this information can be expressed as ______

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 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 ______