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A physical fitness enthusiast decides to devote her exercise time to a combination of jogging and cycling. She wants to earn aerobic points (a measure of the benefit of the exercise to strengthening the heart and lungs) and also to achieve relaxation and enjoyment. She jogs at 6 miles per hour and cycles at 18 miles per hour. An hour of jogging earns 12 aerobic points, and an hour of cycling earns 9 aerobic points. Each week, she would like to earn at least 36 aerobic points, cover at least 54 miles, and cycle at least as many hours as she jogs.
(a) Fill in the accompanying chart.
(b) Let x be the number of hours of jogging and y the number of hours of cycling each week. Referring to the chart, give the inequalities that x and y must satisfy due to miles covered and aerobic points.
(c) Give the inequalities that x and y must satisfy due to her preference for cycling and also due to the fact that x and y cannot be negative.
(d) Express the time spent exercising each week as a linear function of x and y.
(e) Graph the feasible set for the system of linear inequalities
One Hour of Jogging |
One Hour of Cycling |
Requirement |
|
Miles covered Aerobic points |
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