A furniture manufacturer produces two types of display cabinets, type X and type Y. On aweekly basis he must produce at least 2 of each type, but not more than 5 of type X or morethan 6 of type Y. It takes 4 hours to produce type X and 5 hours for type Y in a 40 hourworking week. At least 12 workers are needed with 2 working on type X and 3 on type Y atany one time.

2.1 Represent the above information as a system of inequalities .

2.2 Draw a graph of the system and indicate the feasible region clearly.

2.3 If the profit (P) on type X is R800 and on type Y is R1000, write down the objectivefunction in the form P = ax + by .

2.4 Determine the number of each type that must be produced each week to make amaximum profit. Determine the maximum profit .