The point was to find the cheapest diet for a healthy life. One could argue that we are not talking about healthy foods here, but let’s not bog down with that. The objective function is C=0.90f+0.75e where a piece of chicken costs $0.90 and an ear of corn costs $0.75. Let’s also not bog down about whether those prices are reasonable, even back when UCSMP algebra was written, probably the early 1990s. The vertices of the feasible region, rounded to the nearest hundredth when necessary, are (0, 60/7), (3.76, 2.01), and (5.89, 1.32).
1. No one eats 5.89 pieces of chicken and 1.32 ears of corn. Instruction is needed (but not provided in the example) to help students find the lattice points nearest the vertices of the feasible region, but that are contained in the feasible region. Recall that this is the opening example of linear programming.
2. I sketched the feasible region on graph paper, taking great pains to use a ruler and be accurate. The inequalities were not pleasant to graph. I used the two-intercept method to graph each line, but when one of the boundaries is y=200/151, it took a bit of hand waving to make a good graph.