methods of problem formulation

The data given in the problem can be represented in a table as follows. Let x = number of toys of type-I to be produced y = number of toys of the type - II to be produced \ Total profit = 5x + 3y The LPP formulated for the given problem is: Maximise Z = 5x + 3y su..

There are mainly four steps in the mathematical formulation of linear programming problem as a mathematical model. We will discuss formulation of those problems which involve only two variables. Identify the decision variables and assign symbols x and y to th..

Methods of completing a square and to derive the formula for the solution of the quadratic equation. ..

Step 4: The second integral can be evaluated by method completing square..

Step 3: Resulting integral is evaluated by method of completing squares..

A circular heater is fit around one end of a rod of impure germanium The heater heats a zone or band of the impure rod, it is in contact with The heated zone of germanium melts along with its impurities When the heater gradually shifts to the next zone pure germanium cools and crystalliz..

A small known mass (0.2 to 0.3 g) of the given organic compound is heated with fuming nitric acid and a few crystals of silver nitrate at about 200C in a sealed tube (called Carius tube) for 5 to 6 hours. Carbon and hydrogen are oxidized to carbon dioxide and water while halogen forms a precipitat..

Step 2: Determine L and M Step 4: Integral = Lx + M log (a cos x + bsi..

Put e x f(x) = t Differentiating w.r.t. x, {e x f(x) +e x f ' (x)} dx = dt e x {f(x) + f ' (x)} dx = dt = t + c = e x f(x)+c Evaluate the integral..

P(n,r) is the number of permutations of n dissimilar things taken r at a time. These permutations can be divided into two groups. (i) Those not containing a particular thing l . (ii) Those containing a particular thing l . Taking out l from the given things, we have (n-1) things which can be..