Elementary functions problem
Two varieties of animal feed each contain essential nutrients A and B. Feed I contains 2 units of A and 3 units of B per pound. Feed II contains 2 units of A and 5 units of B per pound. A farmer needs a feed mix that will give his animals a minimum of 16 units of A and 30 units of B. If Feed I costs $3 per pound and Feed II costs $4 per pound, how much of each should be bought to supply the proper nutrition while minimizing cost?
I love this question because it is multiple steps. First the student must decide what x and y are going to represent in the problem. They also must find out how to create the equations and what each will look like. Identifying whether they are maximizing or minimizing, the student will have to decipher the differences between which each means, which inequality symbol we are working with, a cost/profit function and then solve. When solving, the students must distinguish the different possible points of maximums or minimums. Once finding points, they then have to find which one is the correct answer and what that tells us about the problem. This is a multi-step problem that has students problem solving and logically thinking throughout the whole problem.