Question 19.

Now, definitely, three sides should be fenced at Rs 100/ft, and one side should be fenced at Rs 200/ft.

In this question, we are going to assume that the L is greater than B.

Hence, the one side painted at Rs 200/ft should be B to minimise costs.

Hence, the total cost = 200B + 100B + 100L + 100L = 300B + 200L

Now, L x B = 60000

B = 60000/L

Hence, total cost = 300B + 200L = 18000000/L + 200L

To minimise this cost, we can use AM>=GM,

$\frac{\frac{18000000}{L} + 200L}{2} \ge \sqrt{\frac{18000000}{L} \times 200L}$

$\frac{18000000}{L} + 200L \ge 2\sqrt{18000000 \times 200}$

$\frac{18000000}{L} + 200L \ge 2 \times 60000$

Hence, minimum cost = Rs 120000.