Graphical Method of Solving Linear Programming Problems

Q. A fraction becomes 1/4 when 2 is subtracted from the numerator and 3 is added to the denominator. Represent this situation as a linear equation in two variables.

Q. See the figure and write the following:
(i) The Coordinates of $B$.
(ii) The coordinates of $C$.
(iii) The point identified by the coordinates $(-3,-5)$
(iv) The point identified by the coordinates $(2,-4)$.
(v) The abscissa of the point $D$.
(vi) The ordinate of the point $H$.
(vii) The coordinates of the point $L$.
(viii) The coordinates of the point $M$.

Q. Raz was given a linear programming problem to solve in an interview. The constraints of the problems are x ≥ 0, y ≥ 0, 3x+5y ≤ 15, 5x+2y ≤ 10. The interviewer told him one of the four points given below is the optimal solution for the problem and theorem 1 in linear programming would help him to find the answer. Which of the following points is the optimal solution?

1. $(\frac{20}{19},\frac{41}{19})$

2. $(\frac{20}{17},\frac{45}{17})$

3. (1, 1)

4. $(\frac{20}{19},\frac{41}{17})$

5. $(\frac{20}{19},\frac{45}{19})$

Q.

A survey of 1000 farmers found that 600 grew paddy, 350 grew ragi, 280 grew corn, 120 grew paddy and ragi, 100 grew ragi and corn, 80 grew paddy and corn. If each farmer grew at least any one of the above three, then find the number of farmers who grew all the three. ( 3 marks)

Q. If x + y = 4, then find the value of x³ + y³ + 12xy – 64.

Q. Raz was given a linear programming problem to solve in an interview. The constraints of the problems are x ≥ 0, y ≥ 0, 3x+5y ≤ 15, 5x+2y ≤ 10. The interviewer told him one of the four points given below is the optimal solution for the problem and theorem 1 in linear programming would help him to find the answer. Which of the following points is the optimal solution?

1. $(\frac{20}{19},\frac{41}{19})$

2. $(\frac{20}{17},\frac{45}{17})$

3. (1, 1)

4. $(\frac{20}{19},\frac{41}{17})$

5. $(\frac{20}{19},\frac{45}{19})$

Q. What is the value of y which satisfies the following equation?
2y + 9 = 21

1. 15
2. 6
3. 4
4. 10

Q. $p^3{q}^3-pq-p^2{q}^2+p^4{q}^4$ can be regrouped and simplified as _______.

1. $\left(pq\right)(1+pq)(1+pq{)}^2$
2. $(-pq)(1-pq)(1+pq{)}^2$
3. $(-pq)(1-pq)(1+pq{)}^2$
4. $\left(pq\right)(1+pq)(1-pq{)}^2$