Rationalised 2023-24
MATHEMATICAL MODELLING        203
Fig A 2 3
Note that
Z at P (0, 0) = 0
Z at P (20000, 0) = 8 × 20000 = 160000
Z at Q (20000, 6000)  = 8 × 20000 + 7 × 6000 = 202000
Z at R (10500, 34500)  = 8 × 10500 + 7 × 34500 = 325500
Z at S = (5000, 40000) = 8 × 5000 + 7 × 40000 = 320000
Z at T = (0, 40000)  = 7 × 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
M1 medicine and 34500 bottles of M2 medicine in order to get maximum profit of
` 325500