Question

The number of machine parts produced at a manufacturing plant is based on the number of parts made in a given day

and the number of hours worked. Let P = 14x + 100 give the number of parts that are produced since the start of the
shift and H = x be the number of hours that are to be worked that particular day. Create the equation that would give
the number of parts produced per hour.

Answer 1

The equation that would give the number of parts produced per hour,
`P_H` is given as follows;

`P_H` = P/H - 100/H

Explanation:

The given parameters are;

The number of parts produced is given by the equation, P = 14·x + 100, where x represents the number of hours worked on a particular day

The number of hours worked = H

Therefore, we have;

P = 14·H + 100

At H = 0, P₀ = 100

At H = 1, P = 114

At H = 2, P = 128

Therefore, the rate of change of the number of parts produced with the number of hours spent = The number of parts produced per hour, ΔP/ΔH =
`P_H`, is given as follows;

ΔP/ΔH =
`P_H` = (P - P₀)/(H - 0) = P/H - P₀/H = (128 - 100)/(2 - 0) = 14

∴ The number of parts produced per hour,
`P_H` = P/H - 100/H.