
Find all the optimal solution of the LPP in which the objective function is to be minimized subject to the constraints where . Determine also the minimum value of .
Important Questions on Linear Programming Problems



Maximize
Subject to

Maximize
subject to
where, .

Minimize
subject to
where .

A manufacturer has installed three machines to produce two items and (say). Machine and are capable of being operated for at most hours and hours per day. Machine must operate for at least hours a day. To produce a unit of item , the manufacturer has to operate for hours, hour and hours respectively. Machines and are to be used for hour, hours and hours respectively to produce one unit of item . The manufacturer makes a profit of Rs. on each unit of and a profit of Rs. on each unit of item . It is assumed that he can sell out all the items he can produce. Formulate this problem as an LPP in which profit is made maximum.

A factory is engaged in manufacturing two products and which involves lathe work, grinding and assembling. The cutting, grinding and assembling times required for one unit on are and hours respectively. Similarly and hours for one unit of . The profit on and are per unit respectively. Assuming that there are available hours of lathe time, hours of grinding time and hours of assembling time, the manufacturer wants to produce different type of items in such a way that the profit turns out to be maximum. Formulate the above as an LPP.
