Problem:

SIL Computers makes quarterly decisions about their product, that is, notebook computers and desktop computers.  Due to tightness in the market, the supplier has allocated 10,000 processing chips to SIL Computers and each computer requires this chip.  A notebook computer needs a 16MB memory chip sets whilst a desktop computer has 32MB; the company has a stock of 15,000 chip sets to use over the next quarter. Because of tight tolerances, a notebook computer takes more time to assemble: 4 minutes against 3 minutes for a desktop.  There are 25,000 minutes of assembly time available in the next quarter.

Given current market situations, material cost, and our production system, each notebook computer and desktop produced generates Rs. 750 and Rs. 1,000 profit correspondingly.
 
(a). Formulate the problem of finding the  quarterly  production schedule which will maximise the total profit as a linear programming problem, defining the decision variables, constraints and objective function carefully.

(b). Plot the constraints lines for this linear programming problem by drawing a neat sketch graph.  Indicate feasible region, R clearly on your graph.

(c). Verify the feasible corner point (X) at which the optimal solution to this problem is accomplished and evaluate the maximum expected profit.

(d). In brief illustrate the limitations of Linear Programming.