A factory produces four products A,B,C and D which earn $20, $25, $12, and $30 per unit respectively. The factory employs 500 workers who work a 40 hour week. The hours required for each product are set out below: Products A B C D Hours per unit 6 4 2 5 Kgs Material X per unit 2 8.3 5 9 Kgs Material Y per unit 10 4 8 2 Kgs Material Z per unit 1.5 - 2 8 The total availability of materials per week is : X 100 000 Kgs Y 65 000 Kgs Z 220 000 Kgs The company wishes to maximize contribution. Formulate the LP problem in the standard manner.