(Fig A.2.3). The co-ordinates of vertices O, P, Q, R, S and I are (0, 0), (20000, 0), (20000, 6000), (10500, 34500), (5000, 40000) and (0, 40000), respectively. x = 20,000 Rationalised 2023-24 S (5,000, 40,000) MATHEMATICAL MODELLING 203 y=40,000 (0, 40,000) T -R (10,500, 34,500) X'+ P (20,000, 0) Q (20,000, 6,000) NCERT x+v republished Note that Z at P (0, 0) = 0 Z at P (20000, 0) = 8 x 20000 = 160000 Z at Q (20000, 6000) = 8 x 20000 + 7 x 6000 = 202000 Z at R (10500, 34500) = 8 10500+ 7 x 34500 = 325500 Z at S (5000, 40000) = 8 x 5000+ 7 x 40000 = 320000 Z at T = (0, 40000) = 7 x 40000 = 280000 Now observe that the profit is maximum at x = 10500 and y = 34500 and the maximum profit is *325500. Hence, the manufacturer should produce 10500 bottles of M, medicine and 34500 bottles of M, medicine in order to get maximum profit of *325500. Example 6 Suppose a company plans to produce a new product that incur some costs (fixed and variable) and let the company plans to sell the product at a fixed price. Prepare a mathematical model to examine the profitability. Solution Step 1 Situation is clearly identifiable.