Chapter 6.1, Problem 74PE

The purchase price of a home y (in $1000) can be approximated based on the annual income of the buyer $x_1$ (in $1000) and on the square footage of the home $x_2\left({\text{in 100 ft}}^2\right)$ according to $y=a{x}_1+b{x}_2+c$. The table gives the incomes of three buyers, the square footage of the home purchase, and the corresponding purchase prices of the home.

Income ($1000) $x_1$	Square Footage $\left(100{\text{ ft}}^2\right)x_2$	Price ($1000) y
80	21	180
150	28	250
75	18	160

a. Use the data to write a system of leaner equations to solve for a, b, and c.

b. Use a graphing utility to find the reduced row-echelon form the augment matrix.

c. Write the model $y=a{x}_1+b{x}_2+c$.

d. Predict the purchase price for a buyer who makes $100.00 per year and wants a $2500{\text{ ft}}^2$ home.