Question: A residential construction company plans to build several houses of three different types: 5 of type A, 7 of type B, and 12 of type C. Write down a 3-dimensional vector x whose coordinates give the number of houses of each type. Suppose that each house of type A requires 20 units of timber, type B requires 18 units, and type C requires 25 units. Write down a vector u that gives the different timber quantities required for one house of each of the three different types A, B, and C. Find the total timber requirement by computing the inner product u · x.