...recommends that you be sure to get at ? least 300mg of Vitamin P and 90mg of Vitamin Q every day. Back at the 7-11 you see that they have two herbal soporifics: Nature's Slumber, which sells in jars of 100 pills for $4; and Healthy Doze (it's a kind of pun, get it?), which sells in jars of 50 pills for $3. Each Nature's Slumber pill has 200mg of Vitamin P, but only 20 mg of Vitamin Q; while each Healthy Doze pill contains only 100mg of Vitamin P, but 40mg of Vitamin Q. After sneaking a few samples in the store you decide Healthy Doze is much better tasting, and you resolve to take at least as many of that brand every day as of the other.

After retiring to your study for an evening of calculations, you return to 7-11 with a plan. How many pills of each brand will you take every day in order to get your recommended doses at the lowest possible cost? (You may want to cut the pills in half for the optimum combination of the two.)

Solve this one completely: (1) formulate as a linear programming problem; (2) graph the feasible set; and (3) determine the optimum combination.