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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]
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Solution
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
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