The diet problem minimizes the total cost of food necessary to meet some dietary requirements. Consumer buys three foods, say bread, poultry and lettuce which contain various amounts of dietary requirements. For simplicity, let us limits these requirements to carbohydrates (carb.) and proteins (prot.)

whose minimum daily amounts are specified in 200 grams (gr.) of carb. and 80 grams of prot. A 100 gr. of bread (baguette) contains 53 gr. of carb. and 10 gr. of prot. A 100 gr. of poultry (turkey) contains 0 gr. of carb. and 18 gr, of prot. A 100 gr. of lettuce contains 2 gr. of carb. and 1 gr. of prot. The cost of these foods (to the consumer) are: $3 per 300 gr. baguette; $6 per 400 gr.

turkey; $2 per 100 gr. of lettuce (already washed).

a) Formulate the primal LP problem that minimizes the total cost of food necessary to meet the dietary daily requirements. (Primal problems can be minimized. However, the primal constraints are always stated in physical terms.)

b) Write down the dual problem of the consumer and give it a meaningful economic interpretation.

c) Solve the dual problem by graphical methods and state how much the consumer should spend to meet the daily dietary requirements.