Question

Charlie does a weekly exercise program consisting of cardiovascular work and weight training. Each week, he exercises for at least 9 hours. He spends at most 12 hours on weight training. He spends at most 6 hours doing cardiovascular work. Let x denote the time (in hours) that Charlie spends doing cardiovascular work. Let y denote the time (in hours) that he spends on weight training. Shade the region corresponding to all values of x and y that satisfy these requirements.

Answer 1

`(x_1,y_1) = (0,9)`

`(x_2,y_2) = (6,3)`

`(x_3,y_3) = (6,12)`

Explanation:

Given

x = hours spent on cardiovascular work

y = hours spent on weight training

From the first statement,

Each week: he spends at least 9 hours

This is represented as:

`Total \ge 9`

`x + y \ge 9`

From the second statement,

Each week: he spends a max of 12 hours on weights

This is represented as:

`Weight \le 12`

`y \le 12`

From the third statement,

Each week: he spends a max of 6 hours on cardio works

This is represented as:

`Cardio \le 6`

`x \le 6`

So, the inequalities are:

`x + y \ge 9`

`y \le 12`

`x \le 6`

See attachment for the graph where the solution are also highlighted

From the attachment, the solutions are:

`(x_1,y_1) = (0,9)`

`(x_2,y_2) = (6,3)`

`(x_3,y_3) = (6,12)`