The linear programming diet problem is an obvious starting place. For decades linear programs have been used to find optimal combinations of different types of feed for animals such as pigs, cattle and poultry. A popular teaching diet problem is based on McDonald’s fast food. Information on nutritional content and requirements is easily sourced these days on the web. Students can create their own diet problems and find the least cost solution to feed themselves a minimum cost, balanced (within reason) diet at McDonalds. When we used this as a student assignment the solution involved a large number of soft-serve ice cream cones. This sort of solution helps teach students that the computer finds the optimal solution to the model, which may not be even feasible in reality, if there are too many implicit constraints.
A popular variation of the McDonalds diet problem was the Hiking diet problem. This was a little different as the objective was minimising weight rather than cost. Again the initial “optimal” solution lacked variety. (This gave us the opportunity to teach that the number of non-zero variables at optimality will not exceed the number of binding constraints.) The students enjoyed the assignment and some were inspired to the extent that they used it to cater for a hike. Another example was refugee boxes, aiming to provide a balanced diet for a family for a week, at minimum cost.In all these examples the problem of non-integer solutions can also be addressed.
When teaching about fixed and variable costs, and developing a spreadsheet model, our example is that of a sausage sizzle. In it the students are setting up to sell sausages wrapped in bread, with onions, cooked on a barbecue. The aim is to find the breakeven point.
Critical path can be taught in the context of planning a three course dinner.