The document describes several linear programming problems involving constraints and objectives to maximize profit or minimize cost. The problems involve determining optimal production levels of products given constraints on available resources or determining optimal mixtures of ingredients given constraints.

2. A factory manufactures two articles “Chair” and “Table”. For chair a certain machine has to be worked for 3 hours and in addition a craftsman has to work for 4 hours. To manufacture the table, the machine has to be worked for 5 hours and in addition the craftsman has to work for 3 hours. In a week the factory can avail 160 hours of machine time and 140 hours of craftsman’s time. The profit on each chair is Rs.50 and that on each table is Rs.40. If all the articles produced can be sold, then find how many of chairs and tables be produced to earn the maximum profit per week. Formulate the problem as a Linear Programming Problem. Question

3. A company produces three products A, B and C from four raw materials P, Q, R and S. One unit of A requires 2 units of P, 3 units of Q and 4 units of S; one unit of B requires 4 units of Q, 3 units of R and 2 units of S; and one unit of C requires 4 units of P, 3 units of R and 4 units of S. The company has 12 units of material P, 14 units of material Q, 16 units of material R and 18 units of material S. Profit per unit of products A, B and C are Rs.4, Rs.7 and Rs.10 respectively. Formulate the problem as a Linear Programming Problem. Question

4. An electric appliance company produces two products: Refrigerators and ranges. Production takes place in two separate departments I and II. The company’s two products are sold on a weekly basis. The weekly production cannot exceed 25 refrigerators and 35 ranges. The company regularly employs a total of 60 workers in two departments. A refrigerator requires 2 man-weeks labour while a range requires 1 man-week labour. A refrigerator contributes a profit of Rs.60 and a range contributes a profit of Rs.40. Formulate the problem as a Linear Programming Problem. Question