Q.If John drives a car at a speed of 60 kms/hour he has to spend Rs. 5 per km on petrol. If he drives at a faster speed of 90 kms/hour, the cost of petrol increases to Rs. 8 per km. He has Rs. 600 to spend on petrol and wishes to travel the maximum distance within an hour. Formulate the above problem as L.P.P.

Let $x$ = kilometres driven at 60 km/hr and $y$ = kilometres driven at 90 km/hr within the hour. Let $x$ = km driven at 60 km/hr, $y$ = km driven at 90 km/hr. The non-negativity constraints are $x\ge0, y\ge0$ since a negative quantity produced has no meaning. Petrol costs Rs.5/km at the slower speed and Rs.8/km at the faster speed, capped by the Rs.600 budget; the time actually spent driving each portion ($x/60$ hours at the slow speed plus $y/90$ hours at the fast speed) cannot exceed the 1 hour available. The objective to maximize is the total dist …

Step 1: identify the decision variables. Step 2: write the total profit/cost in terms of them — this is the objective function. Step 3: convert each resource limit or minimum requirement given in the problem into one linear inequation; always add the non-negativity constraints $x\ge0,y\ge0$. This ex …

Reversing which product's numbers go with which resource row of the table, or omitting the non-negativity constraints, are the most common formulation errors. Also, minimum-requirement problems (diet/nutrient/strength type) need $\ge$ constraints, while maximum-availability problems (mac …