Materials for Part of the Catalogue

A furniture workshop supplies several showrooms and plans next month's materials with two tables:

• orders[s][p]: pieces of product p ordered by showroom s (one row per showroom, one column per product);
• materials[p][g]: amount of material g (metres of timber, litres of varnish, ...) that one piece of product p uses (one row per product, one column per material).

The matrix product orders $\times$ materials is a showrooms $\times$ materials table: how much of each material every showroom's whole order needs.

The buyers want something finer: the materials needed for only some of the products, for example how much varnish goes into the chairs and the shelves alone, showroom by showroom.

A useful tool here is the outer product. For a column $\mathbf{u}$ with $m$ entries and a row $\mathbf{v}$ with $k$ entries, the outer product $\mathbf{u}\mathbf{v}$ is the $m \times k$ table whose entry in row $i$, column $j$ is $u_i v_j$: every entry of $\mathbf{u}$ times every entry of $\mathbf{v}$.

Task: write catalogue_demand(orders, materials, products) returning the showrooms $\times$ materials table needed to make just the products whose indices are listed in products (no repeats, any order), as a list of rows with every entry rounded to 4 decimal places.

• If products is empty, nothing is made: return a table of zeros of the right shape.
• If products lists every product, the answer is the full product orders $\times$ materials.