Question

Diet of a sick person must contain at least 4000 units of vitamin. Each unit of food F₁ contains 200 units of vitamin, where as each unit of food F₂ contains 100 units of vitamins. Write an inequation to fulfil sick person’s requirements and  represent the solution set graphically.

Answer 1

Let x units of vitamins be consumed in food
F₁ and y units of vitamins are consumed in food F₂ by the sick person.
One unit of food F₁ contains
= 200 units of vitamins
One unit of food F₂ contains
= 100 units of vitamins
Total vitamin consumption = 200x + 100y 
As minimum requirement = 4000 units consumption will either greater than or equal to 4000.
The inequation is 200x + 100y ≥ 4000
or 2x + y ≥ 40, x ≥ 0, y ≥ 0
For drawing the graph, consider 2x + y = 40.
The two points required for the plotting the line are

x	20	0
y	0	40

(20, 0) on X-axis and (0, 40) on Y-axis.
Substitute the coordinate of origin x = 0,
y = 0  in the inequation
2(0) + 0 ≥ 40
⇒ 0 ≥ 40
∴ which is false
∴ all the points on the non-origin side of the line and points on the line satisfy the inequation.
Also, x ≥ 0, y ≥ 0
∴ the solution set is as shown in the figure.