question_answer 18)

A merchant plant to sell two types of personal computers – a desktop model and a portable model that will cost Rs.25,000 and Rs.40,000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant should stock to get maximum profit if he does not want to invest more than Rs.70 lakhs and if his profit on the desktop model is Rs.4500 and on portable model is Rs.5000. 

Answer:

Let number of desktop model computers to stock = x       and number of portable model computers to stock = y       The cost and profit for one unit of a computer of each type is given below :

Computer	Cost	Profit
Desktop	25000	4500
Portable	40000	5000

      Therefore, the above L.P.P. is given as             Maximize, P = 3400 x + 5000 y,       Subject to the constraints x + y                25000 x + 40000 y       i.e. x + y       L1 : x + y = 250        L2 : 5x + 8y = 1400                         Here profit P is maximum at E(250, 50)        For maximum perofit.       Number of desktop model computers = 200       and number of portable model computers = 50