1) Laboratory mice are fed a mixture of two products that contain two important nutrients. Product 1 contains three units of nutrient A and two units nutrient B (per ounce), while product 2 has four units A and five units B. (a) In what proportion should one mix the two products, when mice need as much nutrient A as nutrient B? (b) Assume that there is a need for food with twice the amount of nutrient B in relation to A. Is it possible to satisfy this requirement with the two available products?

2) Assume that A is a (l, p) matrix, B is a (m, q) matrix, and C is a (n, r) matrix. What can you say about l, m, n, p, q, and r if the subsequent products are defined? What are the dimensions of the results? (a) A B C (b) A B^T C (c) B A C^T (d) A^T C B^T