Question

A company requires f(x) number of hours to produce 500 units. It is represented by f(x) = 1800x^–0.4. Find out the number of hours required to produce additional 400 units. [(900)^0.6 = 59.22, (500)^0.6 = 41.63]

Answer 1

f(x) number of hours to produce 500

f(x) = 1800 x^–0.4

The number of hours required to produce additions

400 units = `int_50^((500 + 400)) "f"(x)  "d"x`

= `int_500^900 1800x^(-0.4)  "d"x`

= `int_500^900 x^(-0.4)  "d"x`

= `1800 [(x^(-0.4 + 1))/(- 0.4 + 1)]_500^900`

= `1800 [x^(0.6)/(0.6)]_500^900`

= `1800/0.6[(900)^(0.6) - (500)^(0.6)]`

= `(1800 xx 10)/0.6 xx [59.22 - 41.63]`

= `3000 xx [17.59]`

= ₹ 52770 units