Three Drivers for Every Van

A logistics company predicts how much freight a depot moves per day from two features:

• $x_1$ — number of delivery vans
• $x_2$ — number of drivers on the payroll

Five depots make up the training set:

The model has no bias term: $\hat{y} = w_1x_1 + w_2x_2$, and $X$ is the $5 \times 2$ design matrix whose columns are $x_1$ and $x_2$.

The team tries the normal equations $X^\top X\,w = X^\top y$, finds they cannot be solved, and switches to ridge regression: choose $w$ to minimise

$\lVert y - Xw \rVert^2 + \lambda \lVert w \rVert^2, \qquad \lambda = 50$

whose closed-form solution is

$\hat{w} = (X^\top X + \lambda I)^{-1}X^\top y$

A new depot has just opened, running $6$ vans with $20$ drivers.

How much freight does the ridge model predict for it?

Round your answer to two decimal places.