Question

The cost to produce a certain product depends on 3 main variables, denoted p, q, and r. If C(p, q, r) = C0e−2p + 7q − 9r represents the cost function, find the greatest rate of decrease of this function at the point P0(100, 55, 10).?

Answer 1

Answer:

$\sqrt{134}C_0e^{95}$

Step-by-step explanation:

We are given that the cost function is  given by

$C(p,q,r)=C_0e^{-2p+7q-9r}$

$\nabla C(p,q,r)=< -2C_0e^{-2p+7q-9r},7C_0e^{-2p+7q-9r},-9C_0e^{-2p+7q-9r}>$

We have to find the rate of decrease of this function at the point $P_0(100,55,10)$

$\nabla C(100,55,10)=$

$\nabla C(100, 55,10)=$

$\mid \nabla C(100, 55, 10)\mid=\sqrt{(-2C_0e^{95})^2+(7C_0e^{95})^2+(-9C_0e^{95})^2}$

Greatest rate of decrease of this point at the point $P_0(100,55,10)$ is given by

$\mid \nabla C(100, 55, 10)\mid=\sqrt{134}C_0e^{95}$