Q.A doctor has prescribed two different units of foods A and B to form a weekly diet for a sick person. The minimum requirements of fats, carbohydrates and proteins are 18, 28, 14 units respectively. One unit of food A has 4 units of fats, 14 units of carbohydrates and 8 units of protein. One unit of food B has 6 units of fat, 12 units of carbohydrates and 8 units of protein. The price of food A is 4.5 per unit and that of food B is 3.5 per unit. Form the L.P.P. so that the sick person's diet meets the requirements at a minimum cost.

Formulating an L.P.P. means translating a real-world word problem into the precise mathematical shape of decision variables, an objective function, and a set of constraints. The chapter gives a fixed three-step working rule: Step 1 — identify the decision variables and assign them symbols such as $x,y$ (or $x_1,x_2$), remembering to introduce the non-negativity constraints $x\ge0,y\ge0$; Step 2 — identify what is to be optimized (usually total profit or total cost) and write it as a linear expression in the decision variables — this is the objective function; Step 3 — identify every resource limit or requirement stated in the problem (machine-hours available, raw material availability, minimum nutrient needs, budget, storage space, etc.) and express each one as a linear inequation. A resource that is available only up to some maximum amount gives a $\le$ constraint (e.g. machine-hours, budget, storage space); a requirement that must be met at least to some minimum level gives a $\ge$ constraint (e.g. minimum nutrients in a die …