National university of uzbekistan named after mirzo ulugbek uzbek-israel joint faculty

Figure 1.7.
Example 4 shows how a system of linear inequalities can arise in an applied problem.
Example 4 An Application of a System of Inequalities
The liquid portion of a diet is to provide at least 300 calories, 36 units of vitamin A, and 90 units of vitamin C daily. A cup of dietary drink X provides 60 calories, 12 units of vitamin A, and 10 units of vitamin C. A cup of dietary drink Y provides 60 calories, 6 units of vitamin A, and 30 units of vitamin C. Set up a system of linear inequalities that describes the minimum daily requirements for calories and vitamins.
Solution
x = number of cups of dietary drink X and
y = number of cups of dietary drink Y.
To meet the minimum daily requirements, the inequalities listed below must be satisfied.

For calories:
For vitamin A:
For vitamin C:
The last two inequalities are included because x and y cannot be negative. The graph of this system of linear inequalities is shown at the right	Figure 1.7.

Consider the following problem
Example 5 Subject to the linear conditions
For the line 2x-3y=1
y-intercept: x=0; y=-3
x-intercept: y=0; x=0.5
and for the line x+2y=4 we have
y-intercept: x=0; y=2
x-intercept: y=0; x=4

For the line 2x+y=14
y-intercept: x=0; y=-14
x-intercept: y=0; x=7
for the line -x+2y=8 we have
y-intercept: x=0; y=4
x-intercept: y=0; x=-8
and for the line 2x-y=10
y-intercept: x=0; y=10
x-intercept: y=0; x=5s

For the line 3x+2y=24
y-intercept: x=0; y=-12
x-intercept: y=0; x=8
for the line x+2y=16 we have

y-intercept: x=0; y=8
x-intercept: y=0; x=16
and for the line x+y=9
y-intercept: x=0; y=9
x-intercept: y=0; x=9

2.