A residential company plans to build several houses of three different types: 5

Question

A residential 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 18units, 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 of A, B, and C. Find the timber requirement by computing the inner product u. x 8.

Explanation / Answer

The three dimension vector whoose coordinates give the number of houses

x = [5 7 12]

The vector u will be the number of units of timber required for each type of house

u = [20 18 25]

Taking the dpt product

u.x = [20 18 25]. [5 7 12] = 20 * 5 + 18 * 7 + 25 * 12 = 526

Hence the timber requirement for the houses will be 526 units of timber

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