A carpenter makes tables and chairs from wood and steel. His store has 200 units of wood and 200 units of steel. Each table requires 5 units of wood and 2 units of steel, whereas each chair requires 2 units of wood and 4 units of steel. The demand for the tables is at most 30 and for chairs is at most 35. A table earns a profit of  ₹1,800 and a chair, ₹1,500. If the carpenter produces tables, he has to bear a fixed cost of ₹24,000. Likewise, if the carpenter produces chairs, he must bear a fixed cost of ₹20,000. The store wants to determine the number of tables and chairs it needs to produce to maximize profit.
a. Formulate an integer programming model for this problem.
b. Solve this model by using the computer.