A manufacturing process operates for 10 hours

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

A manufacturing process operates for 10 hours. Its production rate

r(t)

(in units per hour) behaves as follows: • Increases linearly from

0

t=0

to a maximum rate

H

t=2

hours. • Remains constant at

H

from

t=2

t=7

hours. • Decreases linearly from

H

t=7

hours to

0

t=10

hours. If the total number of units produced during the shift is 160, what is the value of

H

? (a)

\dfrac{160}{7}

units per hour (b)

20

units per hour (c)

\dfrac{64}{3}

units per hour (d)

16

units per hour