Question: A door factory can buy supplies in two kinds of packages, \(f\) and \(g\). The package \(f\) contains 3 slabs of wood, 4 fasteners, and 6 brackets. The package \(g\) contains 5 fasteners, 3 brackets, and 7 slabs of wood.

1. Give a list of inputs and outputs for the functions \(f\) and \(g\).
2. Give an order to the 3 kinds of supplies and then write \(f\) and \(g\) as elements of \(\mathbb{R}^{3}\).
3. Let \(L\) be the manufacturing process; it takes in supply packages and gives out two products (doors, and door frames) and it is linear in supplies. If \(Lf\) is 1 door and 2 frames and \(Lg\) is 3 doors and 1 frame, find a matrix for \(\mathrm{L}\).

Price: $2.99

Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document