Kennedy is working two summer jobs, making $11 per hour babysitting and making $8 per hour clearing tables. In a given week, she can work at most 17 total hours and must earn no less than $160. If x represents the number of hours babysitting and y represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution.

Using graphical method of Linear programing problem, the system of inequalities are x + y ≤ 17 and 11x +8y ≥ 160. The maximum value of z=145, x=8,y=14 .

Linear programing problem is" a system of process of finding maximum or minimum value of any variables".

Inequalities is statement of an order relationship, "greater than or greater than or equal to, less than or less than or equal to between two numbers or algebraic expressions" .

According to the question,

Let 'x' represents the number of hours clearing tables and 'y' represents the number of hours clearing tables.

maximum of z =11x+8y

x + y ≤ 17             →     (1)

11x +8y ≥ 160      →       (2)

Using graphical method, we can solve this Linear programing problem(LPP).

In inequality(1) put x=0, we get y=17 and y=0, we get x=17 therefore in equation (1) we get (17,17) draw this point on graph.

In inequality(2) put x=0 we get y=20 and put y=0 we get x=14.54 from equation(2) we get (14.54,20) draw this point on graph.

To find maximum value of z solve this equation

x + y =17            →(3)

11x +8y =160      →(4),

multiply (3) by 8 we get, 8x+8y=136 and subtract the equation (3) from the equation (4)

11x+8y=160

8x+8y=136                               [multiply by(-) on both sides]

we get x=3 substitute this 'x' value in equation (3)

3+y=17

y = 14.

The maximum z = 11x+8y

                         z = 11(3)+8(14)               [substitute (3,14)]

       maximum z =145.

Hence, using graphical method of Linear programing problem, the system of inequalities are x + y ≤ 17 and 11x +8y ≥ 160. The maximum value of z=145, x=8,y=14 .

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