problem1. Four special cases and difficulties arise at times when using graphical approach to solving LP problems. Briefly outline these cases and also illustrate exs with graphical sketches.
problem2. PC Computer Ltd. 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 PC Computer Ltd. and each computer requires a chip. A notebook computer needs a 16MB memory chip sets whilst a desktop computer has 32MB; the company has a stock of 15,000 memory chip sets to use over the next quarter. Due to 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 conditions, material cost, and our production system, each notebook computer and desktop produced generates Rs. 750 and Rs. 1,000 profit respectively.
(i) Formulate the linear programming model for this problem.
(ii) Plot a graph indicating all the constraints, the feasible region (R) and the optimal point (X).
(iii) Solve the LP problem to determine how many of each product should PC Computer Ltd. produce in order to maximise profit for the quarter and evaluate the profit of PC Computer Ltd.
problem3. Outline the limitations of LP?