A vitamin pill $P$ contains $12$ mg iron and $10$ $mg$ zinc. Another pill $Q$ contains $5$ mg iron and $8$ mg zinc. A person needs $80$ mg iron and $100$ mg zinc each month. Pill $P$ costs $4$ dollars and pill $Q$ costs $3$ dollars. How many pills of each type should a person buy to minimize the price while exceeding the monthly requirements?
I have no idea what to do, any help? (Please keep it as simple as possible, this is from a high school textbook before functions are introduced.)
If you don't want to use equations, you will have to use trail and error. Let's see : Say you buy only P pills , need= 10, cost =40. Only Q, need= 16, cost= 48. Since first one costs less, let us try to minimize it further. Take P=9, then Q required=2, cost= 42. Take P=8, then Q required=3, cost= 41. Take P=7, then Q required=4, cost= 40. Take P=6, then Q required=6 (no. of Q increases on account of decreasing iron which is only 5mg per Q pill) , cost= 42.From here, if we decrease P further, the amount of Q required will increase fast because of only 5mg per Q pill. So, the conclusion is that the lowest expense is 40 dollars which can be achieved in 2 ways : 1) 10 P pills. 2) 7 P pills and 4 Q pills.