A patient in the hospital can take two different pain killers, pain killer 1 and pain killer 2. Per dose, pain killer 1 delivers 0.5 units of medicine to the legs and 0.8 units of medicine to the back. Per dose, pain killer 2 delivers 0.7 units of medicine to the legs and 0.4 units of medicine to the back. In, addition pain killer 1 deliver 0.3 units of sleeping medicine and pain killer 2 delivers 0.6 units of sleeping medicine. At most 8 units of sleep medicine should be delivered and at least 4 units of medicine should be delivered to the legs. How many doses of each should be taken to maximize the amount of medicine delivered to the back?