SECTION B: Show all workings to support your answer 30. Consider the following LP problem: Minimize 2x1 +3x2 subject to the constraints xi 0, i = 1,2, and x1 +2x2 4 x1 +x2 3.

(a) Convert this problem to a maximization problem.

(b) Solve the problem of (a) by the graphical method.

31. Use the simplex method to solve the problem: Max Z = x1 +2x3 Sbj. x1 +2x2 +x3 2 x3 1 x1 0, x2 0, x3 0. 32. A company is involved in the production of two items (X and Y). The resources need to produce X and Y are twofold, namely machine time for automatic processing and craftsman time for hand finishing. The table below gives the number of minutes required for each item:

	machine time	craftsman time
item x	13	20
item y	19	29

The company has 40 hours of machine time available in the next working week but only 35 hours of craftsman time. Machine time is costed at K10 per hour worked and craftsman time is costed at K2 per hour worked. Both machine and craftsman idle times incur no costs. The revenue received for each item produced (all production is sold) is K20 for X and K30 for Y. The company has a specific contract to produce 10 items of X per week for a particular customer. Formulate the problem of deciding how much to produce per week as a linear program.