Maximum Profit Rate Criterion:

The criterion is based on maximizing Eq. (7). Substituting Equation (8) and (9) in

(7), we get

                             ---------- (25)

For maximum profit rate,

∂P_r /∂V = 0           ---------------- (25(a))

∂Pr/∂f   = 0       ---------------- (25(b))

Differentiate above Eq. (25) with respect to V and simplify. Then, the condition for maximum profit rate with respect to speed is obtained as Eq. (26).

    ----------- (26)

Similarly, the condition for maximum profit rate with respect to feed is given by

           ------------- (27)

Eqs. (26) and (27) cannot be satisfied simultaneously hence no unique maximum profit rate exists. The conditions for the highest profit rate are found by selecting the maximum possible feed, and then speed corresponding to Eq. (10.26). The method of selecting the cutting conditions when various restrictions apply is similar as discussed in the case of minimum cost per component.