1. A physical fitness enthusiast, Karen, decided to exercise by a combination of jogging and cycling. She jogs at 6 mph and cycles at 18 mph. A measure of the benefit of these activities is given...

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1. A physical fitness enthusiast, Karen, decided to exercise by a combination of jogging and cycling. She jogs at 6 mph and cycles at 18 mph. A measure of the benefit of these activities is given through aerobic points. An hour of jogging gains 4 aerobic points and an hour of cycling gains 3 aerobic points. Each week she would like to earn at least 12 aerobic points, cover at least 54 miles and cycle at least twice as much as she jogs. Formulate a linear programming problem so that Karen minimises the total time spent exercising while achieving her goals. 2. As part of a charity stunt a student wishes to travel around a circular track route in 80 minutes or less. The first five miles are to be travelled on top of a horse-drawn tram and the final three miles in a pink hea rse. If the speeds of tram and hearse are x mph and y mph respectively, write down the constraints for the above. 3. For a dog to remain healthy its daily diet must provide it with at least 2 MJ of energy and at least 0.3 kg of protein but not more than 0.04 kg of salt. There are two items in the diet of most dogs: biscuits and meat. I kg of meat costs $90 and provides 5 MJ of energy, 0.5 kg of protein and 0.04 kg of salt. 1kg of biscuits costs $25 and provides 20 MJ of energy and 0.2 kg of protein and 0.08 kg of salt. Formulate a LP problem to enable you to find the cheapest combination of biscuits and meat In the dogs’s daily diet that will keep him healthy.