Q.The company makes concrete bricks made up of cement and sand. The weight of a concrete brick has to be at least 5 kg. Cement costs Rs.20 per kg. and sand costs Rs.6 per kg. Strength consideration dictate that a concrete brick should contain minimum 4 kg. of cement and not more than 2 kg. of sand. Form the L.P.P. for the cost to be minimum.

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 …